Datasets:
Tasks:
Visual Question Answering
Modalities:
Image
Formats:
imagefolder
Languages:
English
Size:
1K - 10K
License:
File size: 95,416 Bytes
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{"qid": 6200, "type": "numeric", "category_id": 62, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[7, 2], [-6, -5], [-6, -9]], "answer": {"point": [3.4615384615384617, -7.0]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(7, 2), B=(-6, -5), C=(-6, -9). Find the circumcenter.", "im_path": "/images_full/task_06200_circumcircle.png", "im_dots_path": "/images/task_06200_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumcenter?", "image_answer": {"point": [3.4615384615384617, -7.0]}, "choices": null, "image_choices": null}
{"qid": 6201, "type": "numeric", "category_id": 62, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[-3, -3], [-8, 6], [0, -1]], "answer": {"point": [-4.283783783783784, 2.175675675675676]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(-3, -3), B=(-8, 6), C=(0, -1). Find the circumcenter.", "im_path": "/images_full/task_06201_circumcircle.png", "im_dots_path": "/images/task_06201_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumcenter?", "image_answer": {"point": [-4.283783783783784, 2.175675675675676]}, "choices": null, "image_choices": null}
{"qid": 6202, "type": "numeric", "category_id": 62, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[-9, 2], [-10, 7], [-1, -9]], "answer": {"point": [11.879310344827585, 8.775862068965518]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(-9, 2), B=(-10, 7), C=(-1, -9). Find the circumcenter.", "im_path": "/images_full/task_06202_circumcircle.png", "im_dots_path": "/images/task_06202_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumcenter?", "image_answer": {"point": [11.879310344827585, 8.775862068965518]}, "choices": null, "image_choices": null}
{"qid": 6203, "type": "numeric", "category_id": 62, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[-5, 6], [-3, -6], [3, -4]], "answer": {"point": [-1.7894736842105263, 0.3684210526315789]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(-5, 6), B=(-3, -6), C=(3, -4). Find the circumcenter.", "im_path": "/images_full/task_06203_circumcircle.png", "im_dots_path": "/images/task_06203_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumcenter?", "image_answer": {"point": [-1.7894736842105263, 0.3684210526315789]}, "choices": null, "image_choices": null}
{"qid": 6204, "type": "numeric", "category_id": 62, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[1, 4], [-9, 4], [1, 8]], "answer": {"point": [-4.0, 6.0]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(1, 4), B=(-9, 4), C=(1, 8). Find the circumcenter.", "im_path": "/images_full/task_06204_circumcircle.png", "im_dots_path": "/images/task_06204_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumcenter?", "image_answer": {"point": [-4.0, 6.0]}, "choices": null, "image_choices": null}
{"qid": 6205, "type": "numeric", "category_id": 62, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[-1, 8], [5, 10], [2, -2]], "answer": {"point": [3.6818181818181817, 3.9545454545454546]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(-1, 8), B=(5, 10), C=(2, -2). Find the circumcenter.", "im_path": "/images_full/task_06205_circumcircle.png", "im_dots_path": "/images/task_06205_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumcenter?", "image_answer": {"point": [3.6818181818181817, 3.9545454545454546]}, "choices": null, "image_choices": null}
{"qid": 6206, "type": "numeric", "category_id": 62, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[1, 6], [1, 10], [4, 6]], "answer": {"point": [2.5, 8.0]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(1, 6), B=(1, 10), C=(4, 6). Find the circumcenter.", "im_path": "/images_full/task_06206_circumcircle.png", "im_dots_path": "/images/task_06206_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumcenter?", "image_answer": {"point": [2.5, 8.0]}, "choices": null, "image_choices": null}
{"qid": 6207, "type": "numeric", "category_id": 62, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[-1, -4], [-5, 9], [-9, -1]], "answer": {"point": [-3.141304347826087, 2.4565217391304346]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(-1, -4), B=(-5, 9), C=(-9, -1). Find the circumcenter.", "im_path": "/images_full/task_06207_circumcircle.png", "im_dots_path": "/images/task_06207_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumcenter?", "image_answer": {"point": [-3.141304347826087, 2.4565217391304346]}, "choices": null, "image_choices": null}
{"qid": 6208, "type": "numeric", "category_id": 62, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[-2, -8], [3, 1], [7, -4]], "answer": {"point": [1.680327868852459, -4.155737704918033]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(-2, -8), B=(3, 1), C=(7, -4). Find the circumcenter.", "im_path": "/images_full/task_06208_circumcircle.png", "im_dots_path": "/images/task_06208_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumcenter?", "image_answer": {"point": [1.680327868852459, -4.155737704918033]}, "choices": null, "image_choices": null}
{"qid": 6209, "type": "numeric", "category_id": 62, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[6, 9], [-4, 6], [-9, 3]], "answer": {"point": [10.3, -23.5]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(6, 9), B=(-4, 6), C=(-9, 3). Find the circumcenter.", "im_path": "/images_full/task_06209_circumcircle.png", "im_dots_path": "/images/task_06209_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumcenter?", "image_answer": {"point": [10.3, -23.5]}, "choices": null, "image_choices": null}
{"qid": 6210, "type": "numeric", "category_id": 62, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[10, -1], [4, 0], [0, -10]], "answer": {"point": [5.984375, -6.59375]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(10, -1), B=(4, 0), C=(0, -10). Find the circumcenter.", "im_path": "/images_full/task_06210_circumcircle.png", "im_dots_path": "/images/task_06210_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumcenter?", "image_answer": {"point": [5.984375, -6.59375]}, "choices": null, "image_choices": null}
{"qid": 6211, "type": "numeric", "category_id": 62, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[5, -3], [-1, 6], [10, 1]], "answer": {"point": [4.282608695652174, 3.0217391304347827]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(5, -3), B=(-1, 6), C=(10, 1). Find the circumcenter.", "im_path": "/images_full/task_06211_circumcircle.png", "im_dots_path": "/images/task_06211_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumcenter?", "image_answer": {"point": [4.282608695652174, 3.0217391304347827]}, "choices": null, "image_choices": null}
{"qid": 6212, "type": "numeric", "category_id": 62, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[3, -3], [-4, 5], [0, 2]], "answer": {"point": [-10.318181818181818, -7.590909090909091]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(3, -3), B=(-4, 5), C=(0, 2). Find the circumcenter.", "im_path": "/images_full/task_06212_circumcircle.png", "im_dots_path": "/images/task_06212_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumcenter?", "image_answer": {"point": [-10.318181818181818, -7.590909090909091]}, "choices": null, "image_choices": null}
{"qid": 6213, "type": "numeric", "category_id": 62, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[1, -5], [-3, 9], [-5, 10]], "answer": {"point": [-8.875, -0.25]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(1, -5), B=(-3, 9), C=(-5, 10). Find the circumcenter.", "im_path": "/images_full/task_06213_circumcircle.png", "im_dots_path": "/images/task_06213_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumcenter?", "image_answer": {"point": [-8.875, -0.25]}, "choices": null, "image_choices": null}
{"qid": 6214, "type": "numeric", "category_id": 62, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[-1, -4], [7, -10], [-3, 4]], "answer": {"point": [10.615384615384615, 3.1538461538461537]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(-1, -4), B=(7, -10), C=(-3, 4). Find the circumcenter.", "im_path": "/images_full/task_06214_circumcircle.png", "im_dots_path": "/images/task_06214_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumcenter?", "image_answer": {"point": [10.615384615384615, 3.1538461538461537]}, "choices": null, "image_choices": null}
{"qid": 6215, "type": "numeric", "category_id": 62, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[-4, 2], [-7, -1], [9, 9]], "answer": {"point": [17.666666666666668, -22.666666666666668]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(-4, 2), B=(-7, -1), C=(9, 9). Find the circumcenter.", "im_path": "/images_full/task_06215_circumcircle.png", "im_dots_path": "/images/task_06215_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumcenter?", "image_answer": {"point": [17.666666666666668, -22.666666666666668]}, "choices": null, "image_choices": null}
{"qid": 6216, "type": "numeric", "category_id": 62, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[-6, -2], [-3, 7], [-8, -2]], "answer": {"point": [-7.0, 3.3333333333333335]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(-6, -2), B=(-3, 7), C=(-8, -2). Find the circumcenter.", "im_path": "/images_full/task_06216_circumcircle.png", "im_dots_path": "/images/task_06216_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumcenter?", "image_answer": {"point": [-7.0, 3.3333333333333335]}, "choices": null, "image_choices": null}
{"qid": 6217, "type": "numeric", "category_id": 62, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[-8, 1], [-8, -3], [-10, -1]], "answer": {"point": [-8.0, -1.0]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(-8, 1), B=(-8, -3), C=(-10, -1). Find the circumcenter.", "im_path": "/images_full/task_06217_circumcircle.png", "im_dots_path": "/images/task_06217_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumcenter?", "image_answer": {"point": [-8.0, -1.0]}, "choices": null, "image_choices": null}
{"qid": 6218, "type": "numeric", "category_id": 62, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[-3, 1], [4, -6], [7, 0]], "answer": {"point": [1.8333333333333333, -1.1666666666666667]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(-3, 1), B=(4, -6), C=(7, 0). Find the circumcenter.", "im_path": "/images_full/task_06218_circumcircle.png", "im_dots_path": "/images/task_06218_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumcenter?", "image_answer": {"point": [1.8333333333333333, -1.1666666666666667]}, "choices": null, "image_choices": null}
{"qid": 6219, "type": "numeric", "category_id": 62, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[-5, 6], [-9, -1], [-7, 7]], "answer": {"point": [-7.777777777777778, 2.9444444444444446]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(-5, 6), B=(-9, -1), C=(-7, 7). Find the circumcenter.", "im_path": "/images_full/task_06219_circumcircle.png", "im_dots_path": "/images/task_06219_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumcenter?", "image_answer": {"point": [-7.777777777777778, 2.9444444444444446]}, "choices": null, "image_choices": null}
{"qid": 6220, "type": "numeric", "category_id": 62, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[4, 6], [-5, 6], [9, 10]], "answer": {"point": [-0.5, 16.75]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(4, 6), B=(-5, 6), C=(9, 10). Find the circumcenter.", "im_path": "/images_full/task_06220_circumcircle.png", "im_dots_path": "/images/task_06220_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumcenter?", "image_answer": {"point": [-0.5, 16.75]}, "choices": null, "image_choices": null}
{"qid": 6221, "type": "numeric", "category_id": 62, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[-4, 6], [8, -10], [9, -2]], "answer": {"point": [-1.6428571428571428, -4.732142857142857]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(-4, 6), B=(8, -10), C=(9, -2). Find the circumcenter.", "im_path": "/images_full/task_06221_circumcircle.png", "im_dots_path": "/images/task_06221_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumcenter?", "image_answer": {"point": [-1.6428571428571428, -4.732142857142857]}, "choices": null, "image_choices": null}
{"qid": 6222, "type": "numeric", "category_id": 62, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[6, -10], [9, -8], [-6, 8]], "answer": {"point": [1.5, 0.0]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(6, -10), B=(9, -8), C=(-6, 8). Find the circumcenter.", "im_path": "/images_full/task_06222_circumcircle.png", "im_dots_path": "/images/task_06222_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumcenter?", "image_answer": {"point": [1.5, 0.0]}, "choices": null, "image_choices": null}
{"qid": 6223, "type": "numeric", "category_id": 62, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[-3, 8], [4, -3], [-2, -7]], "answer": {"point": [-2.6595744680851063, 0.48936170212765956]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(-3, 8), B=(4, -3), C=(-2, -7). Find the circumcenter.", "im_path": "/images_full/task_06223_circumcircle.png", "im_dots_path": "/images/task_06223_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumcenter?", "image_answer": {"point": [-2.6595744680851063, 0.48936170212765956]}, "choices": null, "image_choices": null}
{"qid": 6224, "type": "numeric", "category_id": 62, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[-9, 4], [9, 3], [1, -8]], "answer": {"point": [-0.1262135922330097, 1.2281553398058251]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(-9, 4), B=(9, 3), C=(1, -8). Find the circumcenter.", "im_path": "/images_full/task_06224_circumcircle.png", "im_dots_path": "/images/task_06224_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumcenter?", "image_answer": {"point": [-0.1262135922330097, 1.2281553398058251]}, "choices": null, "image_choices": null}
{"qid": 6225, "type": "numeric", "category_id": 62, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[2, -9], [6, 1], [-5, 3]], "answer": {"point": [-0.2796610169491525, -2.288135593220339]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(2, -9), B=(6, 1), C=(-5, 3). Find the circumcenter.", "im_path": "/images_full/task_06225_circumcircle.png", "im_dots_path": "/images/task_06225_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumcenter?", "image_answer": {"point": [-0.2796610169491525, -2.288135593220339]}, "choices": null, "image_choices": null}
{"qid": 6226, "type": "numeric", "category_id": 62, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[5, 8], [7, 7], [7, 8]], "answer": {"point": [6.0, 7.5]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(5, 8), B=(7, 7), C=(7, 8). Find the circumcenter.", "im_path": "/images_full/task_06226_circumcircle.png", "im_dots_path": "/images/task_06226_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumcenter?", "image_answer": {"point": [6.0, 7.5]}, "choices": null, "image_choices": null}
{"qid": 6227, "type": "numeric", "category_id": 62, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[-4, -2], [0, -10], [-6, 8]], "answer": {"point": [30.0, 10.0]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(-4, -2), B=(0, -10), C=(-6, 8). Find the circumcenter.", "im_path": "/images_full/task_06227_circumcircle.png", "im_dots_path": "/images/task_06227_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumcenter?", "image_answer": {"point": [30.0, 10.0]}, "choices": null, "image_choices": null}
{"qid": 6228, "type": "numeric", "category_id": 62, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[4, -1], [8, -3], [-6, -9]], "answer": {"point": [2.3846153846153846, -9.23076923076923]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(4, -1), B=(8, -3), C=(-6, -9). Find the circumcenter.", "im_path": "/images_full/task_06228_circumcircle.png", "im_dots_path": "/images/task_06228_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumcenter?", "image_answer": {"point": [2.3846153846153846, -9.23076923076923]}, "choices": null, "image_choices": null}
{"qid": 6229, "type": "numeric", "category_id": 62, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[-6, 0], [3, 4], [-7, -1]], "answer": {"point": [4.5, -11.5]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(-6, 0), B=(3, 4), C=(-7, -1). Find the circumcenter.", "im_path": "/images_full/task_06229_circumcircle.png", "im_dots_path": "/images/task_06229_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumcenter?", "image_answer": {"point": [4.5, -11.5]}, "choices": null, "image_choices": null}
{"qid": 6230, "type": "numeric", "category_id": 62, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[3, -2], [-10, 7], [-2, 8]], "answer": {"point": [-5.088235294117647, 0.20588235294117646]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(3, -2), B=(-10, 7), C=(-2, 8). Find the circumcenter.", "im_path": "/images_full/task_06230_circumcircle.png", "im_dots_path": "/images/task_06230_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumcenter?", "image_answer": {"point": [-5.088235294117647, 0.20588235294117646]}, "choices": null, "image_choices": null}
{"qid": 6231, "type": "numeric", "category_id": 62, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[10, -3], [1, 3], [-6, 1]], "answer": {"point": [0.3, -7.8]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(10, -3), B=(1, 3), C=(-6, 1). Find the circumcenter.", "im_path": "/images_full/task_06231_circumcircle.png", "im_dots_path": "/images/task_06231_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumcenter?", "image_answer": {"point": [0.3, -7.8]}, "choices": null, "image_choices": null}
{"qid": 6232, "type": "numeric", "category_id": 62, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[0, 6], [6, 7], [-2, 0]], "answer": {"point": [3.8529411764705883, 1.3823529411764706]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(0, 6), B=(6, 7), C=(-2, 0). Find the circumcenter.", "im_path": "/images_full/task_06232_circumcircle.png", "im_dots_path": "/images/task_06232_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumcenter?", "image_answer": {"point": [3.8529411764705883, 1.3823529411764706]}, "choices": null, "image_choices": null}
{"qid": 6233, "type": "numeric", "category_id": 62, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[-1, 4], [-10, 2], [-2, 2]], "answer": {"point": [-6.0, 5.25]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(-1, 4), B=(-10, 2), C=(-2, 2). Find the circumcenter.", "im_path": "/images_full/task_06233_circumcircle.png", "im_dots_path": "/images/task_06233_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumcenter?", "image_answer": {"point": [-6.0, 5.25]}, "choices": null, "image_choices": null}
{"qid": 6234, "type": "numeric", "category_id": 62, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[-8, -7], [4, 6], [-5, 6]], "answer": {"point": [-0.5, -1.8846153846153846]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(-8, -7), B=(4, 6), C=(-5, 6). Find the circumcenter.", "im_path": "/images_full/task_06234_circumcircle.png", "im_dots_path": "/images/task_06234_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumcenter?", "image_answer": {"point": [-0.5, -1.8846153846153846]}, "choices": null, "image_choices": null}
{"qid": 6235, "type": "numeric", "category_id": 62, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[4, 3], [9, -8], [3, -6]], "answer": {"point": [7.678571428571429, -1.9642857142857142]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(4, 3), B=(9, -8), C=(3, -6). Find the circumcenter.", "im_path": "/images_full/task_06235_circumcircle.png", "im_dots_path": "/images/task_06235_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumcenter?", "image_answer": {"point": [7.678571428571429, -1.9642857142857142]}, "choices": null, "image_choices": null}
{"qid": 6236, "type": "numeric", "category_id": 62, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[8, -6], [0, 6], [-10, -3]], "answer": {"point": [-0.78125, -3.1875]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(8, -6), B=(0, 6), C=(-10, -3). Find the circumcenter.", "im_path": "/images_full/task_06236_circumcircle.png", "im_dots_path": "/images/task_06236_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumcenter?", "image_answer": {"point": [-0.78125, -3.1875]}, "choices": null, "image_choices": null}
{"qid": 6237, "type": "numeric", "category_id": 62, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[7, 9], [8, -7], [-6, 9]], "answer": {"point": [0.5, 0.5625]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(7, 9), B=(8, -7), C=(-6, 9). Find the circumcenter.", "im_path": "/images_full/task_06237_circumcircle.png", "im_dots_path": "/images/task_06237_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumcenter?", "image_answer": {"point": [0.5, 0.5625]}, "choices": null, "image_choices": null}
{"qid": 6238, "type": "numeric", "category_id": 62, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[2, 5], [-8, -7], [-4, 4]], "answer": {"point": [0.3870967741935484, -3.8225806451612905]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(2, 5), B=(-8, -7), C=(-4, 4). Find the circumcenter.", "im_path": "/images_full/task_06238_circumcircle.png", "im_dots_path": "/images/task_06238_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumcenter?", "image_answer": {"point": [0.3870967741935484, -3.8225806451612905]}, "choices": null, "image_choices": null}
{"qid": 6239, "type": "numeric", "category_id": 62, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[-6, 4], [4, 4], [-8, 6]], "answer": {"point": [-1.0, 11.0]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(-6, 4), B=(4, 4), C=(-8, 6). Find the circumcenter.", "im_path": "/images_full/task_06239_circumcircle.png", "im_dots_path": "/images/task_06239_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumcenter?", "image_answer": {"point": [-1.0, 11.0]}, "choices": null, "image_choices": null}
{"qid": 6240, "type": "numeric", "category_id": 62, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[2, 7], [4, 1], [3, -3]], "answer": {"point": [-5.357142857142857, 1.2142857142857142]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(2, 7), B=(4, 1), C=(3, -3). Find the circumcenter.", "im_path": "/images_full/task_06240_circumcircle.png", "im_dots_path": "/images/task_06240_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumcenter?", "image_answer": {"point": [-5.357142857142857, 1.2142857142857142]}, "choices": null, "image_choices": null}
{"qid": 6241, "type": "numeric", "category_id": 62, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[4, -6], [-1, 4], [4, 6]], "answer": {"point": [3.5, -0.0]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(4, -6), B=(-1, 4), C=(4, 6). Find the circumcenter.", "im_path": "/images_full/task_06241_circumcircle.png", "im_dots_path": "/images/task_06241_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumcenter?", "image_answer": {"point": [3.5, -0.0]}, "choices": null, "image_choices": null}
{"qid": 6242, "type": "numeric", "category_id": 62, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[10, -2], [9, -6], [2, 4]], "answer": {"point": [3.3947368421052633, -2.473684210526316]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(10, -2), B=(9, -6), C=(2, 4). Find the circumcenter.", "im_path": "/images_full/task_06242_circumcircle.png", "im_dots_path": "/images/task_06242_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumcenter?", "image_answer": {"point": [3.3947368421052633, -2.473684210526316]}, "choices": null, "image_choices": null}
{"qid": 6243, "type": "numeric", "category_id": 62, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[-6, 3], [4, -3], [5, -4]], "answer": {"point": [-14.5, -22.5]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(-6, 3), B=(4, -3), C=(5, -4). Find the circumcenter.", "im_path": "/images_full/task_06243_circumcircle.png", "im_dots_path": "/images/task_06243_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumcenter?", "image_answer": {"point": [-14.5, -22.5]}, "choices": null, "image_choices": null}
{"qid": 6244, "type": "numeric", "category_id": 62, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[10, 6], [-9, 0], [3, 4]], "answer": {"point": [69.5, -215.5]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(10, 6), B=(-9, 0), C=(3, 4). Find the circumcenter.", "im_path": "/images_full/task_06244_circumcircle.png", "im_dots_path": "/images/task_06244_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumcenter?", "image_answer": {"point": [69.5, -215.5]}, "choices": null, "image_choices": null}
{"qid": 6245, "type": "numeric", "category_id": 62, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[10, -1], [8, -7], [7, 10]], "answer": {"point": [-5.25, 0.75]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(10, -1), B=(8, -7), C=(7, 10). Find the circumcenter.", "im_path": "/images_full/task_06245_circumcircle.png", "im_dots_path": "/images/task_06245_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumcenter?", "image_answer": {"point": [-5.25, 0.75]}, "choices": null, "image_choices": null}
{"qid": 6246, "type": "numeric", "category_id": 62, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[10, 4], [3, 6], [-7, -2]], "answer": {"point": [3.6315789473684212, -5.0394736842105265]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(10, 4), B=(3, 6), C=(-7, -2). Find the circumcenter.", "im_path": "/images_full/task_06246_circumcircle.png", "im_dots_path": "/images/task_06246_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumcenter?", "image_answer": {"point": [3.6315789473684212, -5.0394736842105265]}, "choices": null, "image_choices": null}
{"qid": 6247, "type": "numeric", "category_id": 62, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[3, 4], [-7, -10], [-10, 3]], "answer": {"point": [-3.058139534883721, -2.244186046511628]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(3, 4), B=(-7, -10), C=(-10, 3). Find the circumcenter.", "im_path": "/images_full/task_06247_circumcircle.png", "im_dots_path": "/images/task_06247_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumcenter?", "image_answer": {"point": [-3.058139534883721, -2.244186046511628]}, "choices": null, "image_choices": null}
{"qid": 6248, "type": "numeric", "category_id": 62, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[9, 3], [10, 6], [-1, 0]], "answer": {"point": [2.388888888888889, 6.87037037037037]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(9, 3), B=(10, 6), C=(-1, 0). Find the circumcenter.", "im_path": "/images_full/task_06248_circumcircle.png", "im_dots_path": "/images/task_06248_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumcenter?", "image_answer": {"point": [2.388888888888889, 6.87037037037037]}, "choices": null, "image_choices": null}
{"qid": 6249, "type": "numeric", "category_id": 62, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[-3, -8], [7, 7], [-7, 4]], "answer": {"point": [1.1666666666666667, 0.05555555555555555]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(-3, -8), B=(7, 7), C=(-7, 4). Find the circumcenter.", "im_path": "/images_full/task_06249_circumcircle.png", "im_dots_path": "/images/task_06249_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumcenter?", "image_answer": {"point": [1.1666666666666667, 0.05555555555555555]}, "choices": null, "image_choices": null}
{"qid": 6250, "type": "numeric", "category_id": 62, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[0, 4], [5, -8], [-9, -1]], "answer": {"point": [-1.605263157894737, -3.710526315789474]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(0, 4), B=(5, -8), C=(-9, -1). Find the circumcenter.", "im_path": "/images_full/task_06250_circumcircle.png", "im_dots_path": "/images/task_06250_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumcenter?", "image_answer": {"point": [-1.605263157894737, -3.710526315789474]}, "choices": null, "image_choices": null}
{"qid": 6251, "type": "numeric", "category_id": 62, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[-2, -7], [-9, -8], [4, -5]], "answer": {"point": [-10.75, 29.25]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(-2, -7), B=(-9, -8), C=(4, -5). Find the circumcenter.", "im_path": "/images_full/task_06251_circumcircle.png", "im_dots_path": "/images/task_06251_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumcenter?", "image_answer": {"point": [-10.75, 29.25]}, "choices": null, "image_choices": null}
{"qid": 6252, "type": "numeric", "category_id": 62, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[6, 6], [-1, 9], [-2, 4]], "answer": {"point": [1.7894736842105263, 5.842105263157895]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(6, 6), B=(-1, 9), C=(-2, 4). Find the circumcenter.", "im_path": "/images_full/task_06252_circumcircle.png", "im_dots_path": "/images/task_06252_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumcenter?", "image_answer": {"point": [1.7894736842105263, 5.842105263157895]}, "choices": null, "image_choices": null}
{"qid": 6253, "type": "numeric", "category_id": 62, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[-4, -8], [-4, 2], [-6, 2]], "answer": {"point": [-5.0, -3.0]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(-4, -8), B=(-4, 2), C=(-6, 2). Find the circumcenter.", "im_path": "/images_full/task_06253_circumcircle.png", "im_dots_path": "/images/task_06253_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumcenter?", "image_answer": {"point": [-5.0, -3.0]}, "choices": null, "image_choices": null}
{"qid": 6254, "type": "numeric", "category_id": 62, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[-7, -8], [-7, 3], [8, -7]], "answer": {"point": [0.16666666666666666, -2.5]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(-7, -8), B=(-7, 3), C=(8, -7). Find the circumcenter.", "im_path": "/images_full/task_06254_circumcircle.png", "im_dots_path": "/images/task_06254_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumcenter?", "image_answer": {"point": [0.16666666666666666, -2.5]}, "choices": null, "image_choices": null}
{"qid": 6255, "type": "numeric", "category_id": 62, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[2, -6], [9, 8], [-6, -10]], "answer": {"point": [-10.5, 9.0]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(2, -6), B=(9, 8), C=(-6, -10). Find the circumcenter.", "im_path": "/images_full/task_06255_circumcircle.png", "im_dots_path": "/images/task_06255_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumcenter?", "image_answer": {"point": [-10.5, 9.0]}, "choices": null, "image_choices": null}
{"qid": 6256, "type": "numeric", "category_id": 62, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[0, -4], [-4, 6], [-6, -6]], "answer": {"point": [-4.647058823529412, -0.058823529411764705]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(0, -4), B=(-4, 6), C=(-6, -6). Find the circumcenter.", "im_path": "/images_full/task_06256_circumcircle.png", "im_dots_path": "/images/task_06256_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumcenter?", "image_answer": {"point": [-4.647058823529412, -0.058823529411764705]}, "choices": null, "image_choices": null}
{"qid": 6257, "type": "numeric", "category_id": 62, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[4, -9], [3, 5], [-2, -6]], "answer": {"point": [3.759259259259259, -1.9814814814814814]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(4, -9), B=(3, 5), C=(-2, -6). Find the circumcenter.", "im_path": "/images_full/task_06257_circumcircle.png", "im_dots_path": "/images/task_06257_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumcenter?", "image_answer": {"point": [3.759259259259259, -1.9814814814814814]}, "choices": null, "image_choices": null}
{"qid": 6258, "type": "numeric", "category_id": 62, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[5, 5], [-10, 0], [-7, -2]], "answer": {"point": [-3.7222222222222223, 6.166666666666667]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(5, 5), B=(-10, 0), C=(-7, -2). Find the circumcenter.", "im_path": "/images_full/task_06258_circumcircle.png", "im_dots_path": "/images/task_06258_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumcenter?", "image_answer": {"point": [-3.7222222222222223, 6.166666666666667]}, "choices": null, "image_choices": null}
{"qid": 6259, "type": "numeric", "category_id": 62, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[6, 6], [1, -7], [5, -2]], "answer": {"point": [-7.092592592592593, 3.574074074074074]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(6, 6), B=(1, -7), C=(5, -2). Find the circumcenter.", "im_path": "/images_full/task_06259_circumcircle.png", "im_dots_path": "/images/task_06259_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumcenter?", "image_answer": {"point": [-7.092592592592593, 3.574074074074074]}, "choices": null, "image_choices": null}
{"qid": 6260, "type": "numeric", "category_id": 62, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[-3, 10], [5, -9], [6, 3]], "answer": {"point": [-5.195652173913044, -2.108695652173913]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(-3, 10), B=(5, -9), C=(6, 3). Find the circumcenter.", "im_path": "/images_full/task_06260_circumcircle.png", "im_dots_path": "/images/task_06260_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumcenter?", "image_answer": {"point": [-5.195652173913044, -2.108695652173913]}, "choices": null, "image_choices": null}
{"qid": 6261, "type": "numeric", "category_id": 62, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[-7, 0], [-3, -8], [-5, 5]], "answer": {"point": [1.7777777777777777, -0.6111111111111112]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(-7, 0), B=(-3, -8), C=(-5, 5). Find the circumcenter.", "im_path": "/images_full/task_06261_circumcircle.png", "im_dots_path": "/images/task_06261_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumcenter?", "image_answer": {"point": [1.7777777777777777, -0.6111111111111112]}, "choices": null, "image_choices": null}
{"qid": 6262, "type": "numeric", "category_id": 62, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[-7, 5], [5, 5], [5, 6]], "answer": {"point": [-1.0, 5.5]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(-7, 5), B=(5, 5), C=(5, 6). Find the circumcenter.", "im_path": "/images_full/task_06262_circumcircle.png", "im_dots_path": "/images/task_06262_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumcenter?", "image_answer": {"point": [-1.0, 5.5]}, "choices": null, "image_choices": null}
{"qid": 6263, "type": "numeric", "category_id": 62, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[4, -7], [8, -4], [-4, 1]], "answer": {"point": [2.357142857142857, -0.6428571428571429]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(4, -7), B=(8, -4), C=(-4, 1). Find the circumcenter.", "im_path": "/images_full/task_06263_circumcircle.png", "im_dots_path": "/images/task_06263_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumcenter?", "image_answer": {"point": [2.357142857142857, -0.6428571428571429]}, "choices": null, "image_choices": null}
{"qid": 6264, "type": "numeric", "category_id": 62, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[6, 3], [1, -8], [-6, 7]], "answer": {"point": [-1.7105263157894737, -0.13157894736842105]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(6, 3), B=(1, -8), C=(-6, 7). Find the circumcenter.", "im_path": "/images_full/task_06264_circumcircle.png", "im_dots_path": "/images/task_06264_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumcenter?", "image_answer": {"point": [-1.7105263157894737, -0.13157894736842105]}, "choices": null, "image_choices": null}
{"qid": 6265, "type": "numeric", "category_id": 62, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[-2, -9], [-3, 4], [4, -10]], "answer": {"point": [2.227272727272727, -2.1363636363636362]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(-2, -9), B=(-3, 4), C=(4, -10). Find the circumcenter.", "im_path": "/images_full/task_06265_circumcircle.png", "im_dots_path": "/images/task_06265_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumcenter?", "image_answer": {"point": [2.227272727272727, -2.1363636363636362]}, "choices": null, "image_choices": null}
{"qid": 6266, "type": "numeric", "category_id": 62, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[2, 9], [-5, 8], [-9, -7]], "answer": {"point": [-0.09405940594059406, -1.3415841584158417]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(2, 9), B=(-5, 8), C=(-9, -7). Find the circumcenter.", "im_path": "/images_full/task_06266_circumcircle.png", "im_dots_path": "/images/task_06266_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumcenter?", "image_answer": {"point": [-0.09405940594059406, -1.3415841584158417]}, "choices": null, "image_choices": null}
{"qid": 6267, "type": "numeric", "category_id": 62, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[-3, 7], [-8, -2], [7, -1]], "answer": {"point": [-0.5846153846153846, -0.23076923076923078]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(-3, 7), B=(-8, -2), C=(7, -1). Find the circumcenter.", "im_path": "/images_full/task_06267_circumcircle.png", "im_dots_path": "/images/task_06267_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumcenter?", "image_answer": {"point": [-0.5846153846153846, -0.23076923076923078]}, "choices": null, "image_choices": null}
{"qid": 6268, "type": "numeric", "category_id": 62, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[-5, 8], [3, 5], [7, -4]], "answer": {"point": [-4.9, -3.9]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(-5, 8), B=(3, 5), C=(7, -4). Find the circumcenter.", "im_path": "/images_full/task_06268_circumcircle.png", "im_dots_path": "/images/task_06268_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumcenter?", "image_answer": {"point": [-4.9, -3.9]}, "choices": null, "image_choices": null}
{"qid": 6269, "type": "numeric", "category_id": 62, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[6, -3], [10, 6], [1, -4]], "answer": {"point": [1.9634146341463414, 4.182926829268292]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(6, -3), B=(10, 6), C=(1, -4). Find the circumcenter.", "im_path": "/images_full/task_06269_circumcircle.png", "im_dots_path": "/images/task_06269_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumcenter?", "image_answer": {"point": [1.9634146341463414, 4.182926829268292]}, "choices": null, "image_choices": null}
{"qid": 6270, "type": "numeric", "category_id": 62, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[-10, -10], [1, 0], [-8, 3]], "answer": {"point": [-5.353658536585366, -4.060975609756097]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(-10, -10), B=(1, 0), C=(-8, 3). Find the circumcenter.", "im_path": "/images_full/task_06270_circumcircle.png", "im_dots_path": "/images/task_06270_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumcenter?", "image_answer": {"point": [-5.353658536585366, -4.060975609756097]}, "choices": null, "image_choices": null}
{"qid": 6271, "type": "numeric", "category_id": 62, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[1, 0], [-3, 8], [-4, 4]], "answer": {"point": [0.8333333333333334, 4.916666666666667]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(1, 0), B=(-3, 8), C=(-4, 4). Find the circumcenter.", "im_path": "/images_full/task_06271_circumcircle.png", "im_dots_path": "/images/task_06271_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumcenter?", "image_answer": {"point": [0.8333333333333334, 4.916666666666667]}, "choices": null, "image_choices": null}
{"qid": 6272, "type": "numeric", "category_id": 62, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[1, 1], [6, 1], [-10, -5]], "answer": {"point": [3.5, -16.666666666666668]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(1, 1), B=(6, 1), C=(-10, -5). Find the circumcenter.", "im_path": "/images_full/task_06272_circumcircle.png", "im_dots_path": "/images/task_06272_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumcenter?", "image_answer": {"point": [3.5, -16.666666666666668]}, "choices": null, "image_choices": null}
{"qid": 6273, "type": "numeric", "category_id": 62, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[-8, 9], [10, -3], [-8, -3]], "answer": {"point": [1.0, 3.0]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(-8, 9), B=(10, -3), C=(-8, -3). Find the circumcenter.", "im_path": "/images_full/task_06273_circumcircle.png", "im_dots_path": "/images/task_06273_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumcenter?", "image_answer": {"point": [1.0, 3.0]}, "choices": null, "image_choices": null}
{"qid": 6274, "type": "numeric", "category_id": 62, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[7, -10], [-6, 5], [5, 3]], "answer": {"point": [-2.0899280575539567, -4.744604316546763]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(7, -10), B=(-6, 5), C=(5, 3). Find the circumcenter.", "im_path": "/images_full/task_06274_circumcircle.png", "im_dots_path": "/images/task_06274_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumcenter?", "image_answer": {"point": [-2.0899280575539567, -4.744604316546763]}, "choices": null, "image_choices": null}
{"qid": 6275, "type": "numeric", "category_id": 62, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[-9, 2], [-2, 10], [2, -4]], "answer": {"point": [-1.5615384615384615, 2.5538461538461537]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(-9, 2), B=(-2, 10), C=(2, -4). Find the circumcenter.", "im_path": "/images_full/task_06275_circumcircle.png", "im_dots_path": "/images/task_06275_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumcenter?", "image_answer": {"point": [-1.5615384615384615, 2.5538461538461537]}, "choices": null, "image_choices": null}
{"qid": 6276, "type": "numeric", "category_id": 62, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[7, 7], [-8, -6], [2, 9]], "answer": {"point": [0.868421052631579, -1.0789473684210527]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(7, 7), B=(-8, -6), C=(2, 9). Find the circumcenter.", "im_path": "/images_full/task_06276_circumcircle.png", "im_dots_path": "/images/task_06276_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumcenter?", "image_answer": {"point": [0.868421052631579, -1.0789473684210527]}, "choices": null, "image_choices": null}
{"qid": 6277, "type": "numeric", "category_id": 62, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[-2, 6], [-5, 10], [-7, 3]], "answer": {"point": [-5.637931034482759, 6.396551724137931]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(-2, 6), B=(-5, 10), C=(-7, 3). Find the circumcenter.", "im_path": "/images_full/task_06277_circumcircle.png", "im_dots_path": "/images/task_06277_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumcenter?", "image_answer": {"point": [-5.637931034482759, 6.396551724137931]}, "choices": null, "image_choices": null}
{"qid": 6278, "type": "numeric", "category_id": 62, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[0, 6], [-4, 10], [-5, 5]], "answer": {"point": [-2.8333333333333335, 7.166666666666667]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(0, 6), B=(-4, 10), C=(-5, 5). Find the circumcenter.", "im_path": "/images_full/task_06278_circumcircle.png", "im_dots_path": "/images/task_06278_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumcenter?", "image_answer": {"point": [-2.8333333333333335, 7.166666666666667]}, "choices": null, "image_choices": null}
{"qid": 6279, "type": "numeric", "category_id": 62, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[-10, 1], [5, 10], [-1, 7]], "answer": {"point": [33.5, -54.5]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(-10, 1), B=(5, 10), C=(-1, 7). Find the circumcenter.", "im_path": "/images_full/task_06279_circumcircle.png", "im_dots_path": "/images/task_06279_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumcenter?", "image_answer": {"point": [33.5, -54.5]}, "choices": null, "image_choices": null}
{"qid": 6280, "type": "numeric", "category_id": 62, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[2, -5], [-8, 4], [3, 3]], "answer": {"point": [-2.848314606741573, -0.33146067415730335]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(2, -5), B=(-8, 4), C=(3, 3). Find the circumcenter.", "im_path": "/images_full/task_06280_circumcircle.png", "im_dots_path": "/images/task_06280_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumcenter?", "image_answer": {"point": [-2.848314606741573, -0.33146067415730335]}, "choices": null, "image_choices": null}
{"qid": 6281, "type": "numeric", "category_id": 62, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[-5, 10], [-5, 9], [-4, 3]], "answer": {"point": [16.5, 9.5]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(-5, 10), B=(-5, 9), C=(-4, 3). Find the circumcenter.", "im_path": "/images_full/task_06281_circumcircle.png", "im_dots_path": "/images/task_06281_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumcenter?", "image_answer": {"point": [16.5, 9.5]}, "choices": null, "image_choices": null}
{"qid": 6282, "type": "numeric", "category_id": 62, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[-7, -3], [-8, 5], [-1, -10]], "answer": {"point": [6.841463414634147, 2.792682926829268]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(-7, -3), B=(-8, 5), C=(-1, -10). Find the circumcenter.", "im_path": "/images_full/task_06282_circumcircle.png", "im_dots_path": "/images/task_06282_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumcenter?", "image_answer": {"point": [6.841463414634147, 2.792682926829268]}, "choices": null, "image_choices": null}
{"qid": 6283, "type": "numeric", "category_id": 62, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[-10, 10], [1, -1], [9, 3]], "answer": {"point": [0.6666666666666666, 9.666666666666666]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(-10, 10), B=(1, -1), C=(9, 3). Find the circumcenter.", "im_path": "/images_full/task_06283_circumcircle.png", "im_dots_path": "/images/task_06283_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumcenter?", "image_answer": {"point": [0.6666666666666666, 9.666666666666666]}, "choices": null, "image_choices": null}
{"qid": 6284, "type": "numeric", "category_id": 62, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[9, 0], [-4, 4], [5, -4]], "answer": {"point": [2.6176470588235294, 2.3823529411764706]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(9, 0), B=(-4, 4), C=(5, -4). Find the circumcenter.", "im_path": "/images_full/task_06284_circumcircle.png", "im_dots_path": "/images/task_06284_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumcenter?", "image_answer": {"point": [2.6176470588235294, 2.3823529411764706]}, "choices": null, "image_choices": null}
{"qid": 6285, "type": "numeric", "category_id": 62, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[0, 8], [4, 10], [-9, 8]], "answer": {"point": [-4.5, 22.0]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(0, 8), B=(4, 10), C=(-9, 8). Find the circumcenter.", "im_path": "/images_full/task_06285_circumcircle.png", "im_dots_path": "/images/task_06285_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumcenter?", "image_answer": {"point": [-4.5, 22.0]}, "choices": null, "image_choices": null}
{"qid": 6286, "type": "numeric", "category_id": 62, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[-10, 8], [2, -7], [-10, -7]], "answer": {"point": [-4.0, 0.5]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(-10, 8), B=(2, -7), C=(-10, -7). Find the circumcenter.", "im_path": "/images_full/task_06286_circumcircle.png", "im_dots_path": "/images/task_06286_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumcenter?", "image_answer": {"point": [-4.0, 0.5]}, "choices": null, "image_choices": null}
{"qid": 6287, "type": "numeric", "category_id": 62, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[-8, 5], [7, 2], [8, 8]], "answer": {"point": [0.04838709677419355, 6.241935483870968]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(-8, 5), B=(7, 2), C=(8, 8). Find the circumcenter.", "im_path": "/images_full/task_06287_circumcircle.png", "im_dots_path": "/images/task_06287_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumcenter?", "image_answer": {"point": [0.04838709677419355, 6.241935483870968]}, "choices": null, "image_choices": null}
{"qid": 6288, "type": "numeric", "category_id": 62, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[-6, 0], [-4, 0], [0, -3]], "answer": {"point": [-5.0, -5.5]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(-6, 0), B=(-4, 0), C=(0, -3). Find the circumcenter.", "im_path": "/images_full/task_06288_circumcircle.png", "im_dots_path": "/images/task_06288_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumcenter?", "image_answer": {"point": [-5.0, -5.5]}, "choices": null, "image_choices": null}
{"qid": 6289, "type": "numeric", "category_id": 62, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[6, -5], [10, -3], [7, 3]], "answer": {"point": [6.5, -1.0]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(6, -5), B=(10, -3), C=(7, 3). Find the circumcenter.", "im_path": "/images_full/task_06289_circumcircle.png", "im_dots_path": "/images/task_06289_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumcenter?", "image_answer": {"point": [6.5, -1.0]}, "choices": null, "image_choices": null}
{"qid": 6290, "type": "numeric", "category_id": 62, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[0, 6], [-6, -5], [3, -7]], "answer": {"point": [-0.3738738738738739, -0.9324324324324325]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(0, 6), B=(-6, -5), C=(3, -7). Find the circumcenter.", "im_path": "/images_full/task_06290_circumcircle.png", "im_dots_path": "/images/task_06290_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumcenter?", "image_answer": {"point": [-0.3738738738738739, -0.9324324324324325]}, "choices": null, "image_choices": null}
{"qid": 6291, "type": "numeric", "category_id": 62, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[8, -2], [-6, 4], [3, 7]], "answer": {"point": [0.4375, -0.3125]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(8, -2), B=(-6, 4), C=(3, 7). Find the circumcenter.", "im_path": "/images_full/task_06291_circumcircle.png", "im_dots_path": "/images/task_06291_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumcenter?", "image_answer": {"point": [0.4375, -0.3125]}, "choices": null, "image_choices": null}
{"qid": 6292, "type": "numeric", "category_id": 62, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[7, 3], [-1, 3], [-5, -1]], "answer": {"point": [3.0, -5.0]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(7, 3), B=(-1, 3), C=(-5, -1). Find the circumcenter.", "im_path": "/images_full/task_06292_circumcircle.png", "im_dots_path": "/images/task_06292_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumcenter?", "image_answer": {"point": [3.0, -5.0]}, "choices": null, "image_choices": null}
{"qid": 6293, "type": "numeric", "category_id": 62, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[-8, -2], [-1, 2], [-3, 6]], "answer": {"point": [-5.722222222222222, 2.138888888888889]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(-8, -2), B=(-1, 2), C=(-3, 6). Find the circumcenter.", "im_path": "/images_full/task_06293_circumcircle.png", "im_dots_path": "/images/task_06293_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumcenter?", "image_answer": {"point": [-5.722222222222222, 2.138888888888889]}, "choices": null, "image_choices": null}
{"qid": 6294, "type": "numeric", "category_id": 62, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[5, -2], [7, 8], [9, 7]], "answer": {"point": [5.7727272727272725, 3.0454545454545454]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(5, -2), B=(7, 8), C=(9, 7). Find the circumcenter.", "im_path": "/images_full/task_06294_circumcircle.png", "im_dots_path": "/images/task_06294_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumcenter?", "image_answer": {"point": [5.7727272727272725, 3.0454545454545454]}, "choices": null, "image_choices": null}
{"qid": 6295, "type": "numeric", "category_id": 62, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[-9, -4], [0, 8], [10, 9]], "answer": {"point": [6.472972972972973, -6.22972972972973]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(-9, -4), B=(0, 8), C=(10, 9). Find the circumcenter.", "im_path": "/images_full/task_06295_circumcircle.png", "im_dots_path": "/images/task_06295_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumcenter?", "image_answer": {"point": [6.472972972972973, -6.22972972972973]}, "choices": null, "image_choices": null}
{"qid": 6296, "type": "numeric", "category_id": 62, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[-10, -9], [10, -1], [3, 5]], "answer": {"point": [0.1590909090909091, -5.3977272727272725]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(-10, -9), B=(10, -1), C=(3, 5). Find the circumcenter.", "im_path": "/images_full/task_06296_circumcircle.png", "im_dots_path": "/images/task_06296_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumcenter?", "image_answer": {"point": [0.1590909090909091, -5.3977272727272725]}, "choices": null, "image_choices": null}
{"qid": 6297, "type": "numeric", "category_id": 62, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[9, 8], [-5, 9], [4, 2]], "answer": {"point": [2.0168539325842696, 8.735955056179776]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(9, 8), B=(-5, 9), C=(4, 2). Find the circumcenter.", "im_path": "/images_full/task_06297_circumcircle.png", "im_dots_path": "/images/task_06297_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumcenter?", "image_answer": {"point": [2.0168539325842696, 8.735955056179776]}, "choices": null, "image_choices": null}
{"qid": 6298, "type": "numeric", "category_id": 62, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[6, 8], [7, 1], [0, -2]], "answer": {"point": [1.6538461538461537, 3.8076923076923075]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(6, 8), B=(7, 1), C=(0, -2). Find the circumcenter.", "im_path": "/images_full/task_06298_circumcircle.png", "im_dots_path": "/images/task_06298_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumcenter?", "image_answer": {"point": [1.6538461538461537, 3.8076923076923075]}, "choices": null, "image_choices": null}
{"qid": 6299, "type": "numeric", "category_id": 62, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[-5, 3], [-9, -6], [7, -2]], "answer": {"point": [-0.953125, -4.1875]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(-5, 3), B=(-9, -6), C=(7, -2). Find the circumcenter.", "im_path": "/images_full/task_06299_circumcircle.png", "im_dots_path": "/images/task_06299_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumcenter?", "image_answer": {"point": [-0.953125, -4.1875]}, "choices": null, "image_choices": null}
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