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jamescai20
/
tts-reasoning

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2 values
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dict
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dict
advanced_geometry/incircle_radius
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nConsider triangle ABC with coordinates A=(-4, 8), B=(-8, -8), and C=(-8, 5). Compute the radius of its incircle. Show your work in <think> </think> tags. Round the radius to 3 decimal places and return it in <answer> </answer> tags, for example <answer> 2.176 </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "1.508", "style": "rule" }
{ "index": 300, "split": "train" }
advanced_geometry/incircle_radius
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nFind the incircle radius of triangle ABC whose vertices are A=(5, -5), B=(4, 8), and C=(-8, 6). Show your work in <think> </think> tags. Round the radius to 3 decimal places and return it in <answer> </answer> tags, for example <answer> 2.176 </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "3.741", "style": "rule" }
{ "index": 301, "split": "train" }
advanced_geometry/orthocenter
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nFor triangle with vertices A=(2, -7), B=(-1, 6), and C=(9, 0), determine the orthocenter (intersection of altitudes). Show your work in <think> </think> tags. Round the coordinates to 3 decimal places and return them inside parenthesis in <answer> </answer>, for example <answer> (0.304, 1.217) </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "(5.750, -0.750)", "style": "rule" }
{ "index": 302, "split": "train" }
advanced_geometry/orthocenter
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nGiven triangle ABC with coordinates A=(-10, -5), B=(3, -7), and C=(-4, 1), find the coordinates of its orthocenter. Show your work in <think> </think> tags. Round the coordinates to 3 decimal places and return them inside parenthesis in <answer> </answer>, for example <answer> (0.304, 1.217) </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "(-4.133, 0.133)", "style": "rule" }
{ "index": 303, "split": "train" }
advanced_geometry/angle_measure
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nGiven a triangle with vertices A=(-4, 9), B=(6, -7), and C=(7, 0), determine the angle at B in degrees. Show your work in <think> </think> tags. Round the angle degrees to 2 decimal places, append a degree symbol, and return it in <answer> </answer> tags, for example <answer> 17.10° </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "40.14°", "style": "rule" }
{ "index": 304, "split": "train" }
advanced_geometry/orthocenter
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nFor triangle with vertices A=(9, 5), B=(-2, 5), and C=(-4, -3), determine the orthocenter (intersection of altitudes). Show your work in <think> </think> tags. Round the coordinates to 3 decimal places and return them inside parenthesis in <answer> </answer>, for example <answer> (0.304, 1.217) </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "(-4.000, 8.250)", "style": "rule" }
{ "index": 305, "split": "train" }
advanced_geometry/orthocenter
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nGiven triangle ABC with coordinates A=(-5, -4), B=(-3, 4), and C=(1, -8), find the coordinates of its orthocenter. Show your work in <think> </think> tags. Round the coordinates to 3 decimal places and return them inside parenthesis in <answer> </answer>, for example <answer> (0.304, 1.217) </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "(-9.286, -5.429)", "style": "rule" }
{ "index": 306, "split": "train" }
advanced_geometry/orthocenter
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nFor triangle with vertices A=(6, 3), B=(-1, 2), and C=(8, -2), determine the orthocenter (intersection of altitudes). Show your work in <think> </think> tags. Round the coordinates to 3 decimal places and return them inside parenthesis in <answer> </answer>, for example <answer> (0.304, 1.217) </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "(6.973, 5.189)", "style": "rule" }
{ "index": 307, "split": "train" }
advanced_geometry/orthocenter
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nGiven triangle ABC with coordinates A=(-5, 2), B=(0, 10), and C=(1, -2), find the coordinates of its orthocenter. Show your work in <think> </think> tags. Round the coordinates to 3 decimal places and return them inside parenthesis in <answer> </answer>, for example <answer> (0.304, 1.217) </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "(-5.353, 1.971)", "style": "rule" }
{ "index": 308, "split": "train" }
advanced_geometry/angle_measure
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nGiven a triangle with vertices A=(8, 1), B=(0, -2), and C=(0, -1), determine the angle at B in degrees. Show your work in <think> </think> tags. Round the angle degrees to 2 decimal places, append a degree symbol, and return it in <answer> </answer> tags, for example <answer> 17.10° </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "69.44°", "style": "rule" }
{ "index": 309, "split": "train" }
advanced_geometry/orthocenter
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nFor triangle with vertices A=(-6, -8), B=(-2, -6), and C=(8, -4), determine the orthocenter (intersection of altitudes). Show your work in <think> </think> tags. Round the coordinates to 3 decimal places and return them inside parenthesis in <answer> </answer>, for example <answer> (0.304, 1.217) </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "(-16.667, 45.333)", "style": "rule" }
{ "index": 310, "split": "train" }
advanced_geometry/incircle_radius
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nConsider triangle ABC with coordinates A=(-8, 2), B=(-8, 9), and C=(5, 2). Compute the radius of its incircle. Show your work in <think> </think> tags. Round the radius to 3 decimal places and return it in <answer> </answer> tags, for example <answer> 2.176 </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "2.618", "style": "rule" }
{ "index": 311, "split": "train" }
advanced_geometry/incircle_radius
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nConsider triangle ABC with coordinates A=(-4, -8), B=(-7, 10), and C=(-6, -10). Compute the radius of its incircle. Show your work in <think> </think> tags. Round the radius to 3 decimal places and return it in <answer> </answer> tags, for example <answer> 2.176 </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "1.022", "style": "rule" }
{ "index": 312, "split": "train" }
advanced_geometry/incircle_radius
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nConsider triangle ABC with coordinates A=(-7, 9), B=(2, 0), and C=(-9, -6). Compute the radius of its incircle. Show your work in <think> </think> tags. Round the radius to 3 decimal places and return it in <answer> </answer> tags, for example <answer> 2.176 </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "3.788", "style": "rule" }
{ "index": 313, "split": "train" }
advanced_geometry/angle_measure
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nGiven a triangle with vertices A=(-9, 5), B=(-2, 3), and C=(3, 9), determine the angle at B in degrees. Show your work in <think> </think> tags. Round the angle degrees to 2 decimal places, append a degree symbol, and return it in <answer> </answer> tags, for example <answer> 17.10° </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "113.86°", "style": "rule" }
{ "index": 314, "split": "train" }
advanced_geometry/incircle_radius
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nConsider triangle ABC with coordinates A=(1, -8), B=(-5, -3), and C=(-2, -6). Compute the radius of its incircle. Show your work in <think> </think> tags. Round the radius to 3 decimal places and return it in <answer> </answer> tags, for example <answer> 2.176 </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "0.192", "style": "rule" }
{ "index": 315, "split": "train" }
advanced_geometry/incircle_radius
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nConsider triangle ABC with coordinates A=(-4, 2), B=(-1, -4), and C=(-10, -7). Compute the radius of its incircle. Show your work in <think> </think> tags. Round the radius to 3 decimal places and return it in <answer> </answer> tags, for example <answer> 2.176 </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "2.332", "style": "rule" }
{ "index": 316, "split": "train" }
advanced_geometry/incircle_radius
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nFind the incircle radius of triangle ABC whose vertices are A=(6, 2), B=(8, 5), and C=(8, -1). Show your work in <think> </think> tags. Round the radius to 3 decimal places and return it in <answer> </answer> tags, for example <answer> 2.176 </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "0.908", "style": "rule" }
{ "index": 317, "split": "train" }
advanced_geometry/incircle_radius
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nConsider triangle ABC with coordinates A=(-1, -3), B=(-8, -4), and C=(-6, 7). Compute the radius of its incircle. Show your work in <think> </think> tags. Round the radius to 3 decimal places and return it in <answer> </answer> tags, for example <answer> 2.176 </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "2.548", "style": "rule" }
{ "index": 318, "split": "train" }
advanced_geometry/angle_measure
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nIn triangle ABC with coordinates A=(-6, 2), B=(2, 4), and C=(-10, 3), find the measure (in degrees) of angle ABC. Show your work in <think> </think> tags. Round the angle degrees to 2 decimal places, append a degree symbol, and return it in <answer> </answer> tags, for example <answer> 17.10° </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "9.27°", "style": "rule" }
{ "index": 319, "split": "train" }
advanced_geometry/angle_measure
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nGiven a triangle with vertices A=(6, 9), B=(1, -3), and C=(6, 10), determine the angle at B in degrees. Show your work in <think> </think> tags. Round the angle degrees to 2 decimal places, append a degree symbol, and return it in <answer> </answer> tags, for example <answer> 17.10° </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "1.58°", "style": "rule" }
{ "index": 320, "split": "train" }
advanced_geometry/incircle_radius
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nFind the incircle radius of triangle ABC whose vertices are A=(-9, 7), B=(-5, -1), and C=(-8, -8). Show your work in <think> </think> tags. Round the radius to 3 decimal places and return it in <answer> </answer> tags, for example <answer> 2.176 </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "1.646", "style": "rule" }
{ "index": 321, "split": "train" }
advanced_geometry/incircle_radius
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nConsider triangle ABC with coordinates A=(-8, 5), B=(-10, -10), and C=(-5, 0). Compute the radius of its incircle. Show your work in <think> </think> tags. Round the radius to 3 decimal places and return it in <answer> </answer> tags, for example <answer> 2.176 </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "1.711", "style": "rule" }
{ "index": 322, "split": "train" }
advanced_geometry/angle_measure
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nGiven a triangle with vertices A=(-1, -6), B=(-1, 9), and C=(-4, 6), determine the angle at B in degrees. Show your work in <think> </think> tags. Round the angle degrees to 2 decimal places, append a degree symbol, and return it in <answer> </answer> tags, for example <answer> 17.10° </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "45.00°", "style": "rule" }
{ "index": 323, "split": "train" }
advanced_geometry/incircle_radius
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nFind the incircle radius of triangle ABC whose vertices are A=(5, -7), B=(-6, 6), and C=(2, 2). Show your work in <think> </think> tags. Round the radius to 3 decimal places and return it in <answer> </answer> tags, for example <answer> 2.176 </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "1.692", "style": "rule" }
{ "index": 324, "split": "train" }
advanced_geometry/incircle_radius
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nFind the incircle radius of triangle ABC whose vertices are A=(6, 5), B=(-10, 1), and C=(-3, -10). Show your work in <think> </think> tags. Round the radius to 3 decimal places and return it in <answer> </answer> tags, for example <answer> 2.176 </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "4.338", "style": "rule" }
{ "index": 325, "split": "train" }
advanced_geometry/orthocenter
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nFor triangle with vertices A=(8, -9), B=(-9, -4), and C=(-7, 5), determine the orthocenter (intersection of altitudes). Show your work in <think> </think> tags. Round the coordinates to 3 decimal places and return them inside parenthesis in <answer> </answer>, for example <answer> (0.304, 1.217) </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "(-9.945, -5.012)", "style": "rule" }
{ "index": 326, "split": "train" }
advanced_geometry/orthocenter
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nGiven triangle ABC with coordinates A=(-1, -3), B=(9, -9), and C=(-10, 3), find the coordinates of its orthocenter. Show your work in <think> </think> tags. Round the coordinates to 3 decimal places and return them inside parenthesis in <answer> </answer>, for example <answer> (0.304, 1.217) </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "(-253.000, -402.000)", "style": "rule" }
{ "index": 327, "split": "train" }
advanced_geometry/incircle_radius
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nFind the incircle radius of triangle ABC whose vertices are A=(10, -1), B=(8, 6), and C=(-2, -8). Show your work in <think> </think> tags. Round the radius to 3 decimal places and return it in <answer> </answer> tags, for example <answer> 2.176 </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "2.554", "style": "rule" }
{ "index": 328, "split": "train" }
advanced_geometry/orthocenter
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nFor triangle with vertices A=(9, 3), B=(3, 9), and C=(-7, -3), determine the orthocenter (intersection of altitudes). Show your work in <think> </think> tags. Round the coordinates to 3 decimal places and return them inside parenthesis in <answer> </answer>, for example <answer> (0.304, 1.217) </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "(3.545, 7.545)", "style": "rule" }
{ "index": 329, "split": "train" }
advanced_geometry/incircle_radius
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nFind the incircle radius of triangle ABC whose vertices are A=(1, -3), B=(-8, 6), and C=(-4, 4). Show your work in <think> </think> tags. Round the radius to 3 decimal places and return it in <answer> </answer> tags, for example <answer> 2.176 </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "0.698", "style": "rule" }
{ "index": 330, "split": "train" }
advanced_geometry/incircle_radius
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nFind the incircle radius of triangle ABC whose vertices are A=(-7, -7), B=(-4, -3), and C=(9, 9). Show your work in <think> </think> tags. Round the radius to 3 decimal places and return it in <answer> </answer> tags, for example <answer> 2.176 </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "0.353", "style": "rule" }
{ "index": 331, "split": "train" }
advanced_geometry/orthocenter
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nGiven triangle ABC with coordinates A=(-6, 6), B=(-6, -6), and C=(6, 7), find the coordinates of its orthocenter. Show your work in <think> </think> tags. Round the coordinates to 3 decimal places and return them inside parenthesis in <answer> </answer>, for example <answer> (0.304, 1.217) </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "(-7.083, 7.000)", "style": "rule" }
{ "index": 332, "split": "train" }
advanced_geometry/incircle_radius
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nFind the incircle radius of triangle ABC whose vertices are A=(1, -3), B=(3, -5), and C=(-2, -5). Show your work in <think> </think> tags. Round the radius to 3 decimal places and return it in <answer> </answer> tags, for example <answer> 2.176 </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "0.875", "style": "rule" }
{ "index": 333, "split": "train" }
advanced_geometry/angle_measure
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nGiven a triangle with vertices A=(2, 5), B=(-1, -5), and C=(6, -7), determine the angle at B in degrees. Show your work in <think> </think> tags. Round the angle degrees to 2 decimal places, append a degree symbol, and return it in <answer> </answer> tags, for example <answer> 17.10° </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "89.25°", "style": "rule" }
{ "index": 334, "split": "train" }
advanced_geometry/incircle_radius
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nConsider triangle ABC with coordinates A=(6, -7), B=(-3, -8), and C=(-10, 5). Compute the radius of its incircle. Show your work in <think> </think> tags. Round the radius to 3 decimal places and return it in <answer> </answer> tags, for example <answer> 2.176 </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "2.830", "style": "rule" }
{ "index": 335, "split": "train" }
advanced_geometry/incircle_radius
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nConsider triangle ABC with coordinates A=(-1, 2), B=(4, -6), and C=(4, 3). Compute the radius of its incircle. Show your work in <think> </think> tags. Round the radius to 3 decimal places and return it in <answer> </answer> tags, for example <answer> 2.176 </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "1.912", "style": "rule" }
{ "index": 336, "split": "train" }
advanced_geometry/incircle_radius
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nFind the incircle radius of triangle ABC whose vertices are A=(-4, 7), B=(6, 0), and C=(8, 0). Show your work in <think> </think> tags. Round the radius to 3 decimal places and return it in <answer> </answer> tags, for example <answer> 2.176 </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "0.498", "style": "rule" }
{ "index": 337, "split": "train" }
advanced_geometry/incircle_radius
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nConsider triangle ABC with coordinates A=(0, 8), B=(3, 7), and C=(4, -3). Compute the radius of its incircle. Show your work in <think> </think> tags. Round the radius to 3 decimal places and return it in <answer> </answer> tags, for example <answer> 2.176 </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "1.164", "style": "rule" }
{ "index": 338, "split": "train" }
advanced_geometry/orthocenter
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nGiven triangle ABC with coordinates A=(5, 8), B=(-10, -4), and C=(-7, -1), find the coordinates of its orthocenter. Show your work in <think> </think> tags. Round the coordinates to 3 decimal places and return them inside parenthesis in <answer> </answer>, for example <answer> (0.304, 1.217) </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "(-91.000, 104.000)", "style": "rule" }
{ "index": 339, "split": "train" }
advanced_geometry/incircle_radius
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nFind the incircle radius of triangle ABC whose vertices are A=(-2, -6), B=(0, -3), and C=(6, -9). Show your work in <think> </think> tags. Round the radius to 3 decimal places and return it in <answer> </answer> tags, for example <answer> 2.176 </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "1.454", "style": "rule" }
{ "index": 340, "split": "train" }
advanced_geometry/angle_measure
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nGiven a triangle with vertices A=(6, 2), B=(-6, -3), and C=(5, -7), determine the angle at B in degrees. Show your work in <think> </think> tags. Round the angle degrees to 2 decimal places, append a degree symbol, and return it in <answer> </answer> tags, for example <answer> 17.10° </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "42.60°", "style": "rule" }
{ "index": 341, "split": "train" }
advanced_geometry/angle_measure
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nIn triangle ABC with coordinates A=(2, -9), B=(7, -10), and C=(10, 1), find the measure (in degrees) of angle ABC. Show your work in <think> </think> tags. Round the angle degrees to 2 decimal places, append a degree symbol, and return it in <answer> </answer> tags, for example <answer> 17.10° </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "93.95°", "style": "rule" }
{ "index": 342, "split": "train" }
advanced_geometry/incircle_radius
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nConsider triangle ABC with coordinates A=(5, 2), B=(6, -1), and C=(-10, 2). Compute the radius of its incircle. Show your work in <think> </think> tags. Round the radius to 3 decimal places and return it in <answer> </answer> tags, for example <answer> 2.176 </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "1.307", "style": "rule" }
{ "index": 343, "split": "train" }
advanced_geometry/angle_measure
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nIn triangle ABC with coordinates A=(-1, 2), B=(7, 4), and C=(3, -9), find the measure (in degrees) of angle ABC. Show your work in <think> </think> tags. Round the angle degrees to 2 decimal places, append a degree symbol, and return it in <answer> </answer> tags, for example <answer> 17.10° </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "58.86°", "style": "rule" }
{ "index": 344, "split": "train" }
advanced_geometry/orthocenter
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nFor triangle with vertices A=(-4, -9), B=(-5, -4), and C=(-4, 1), determine the orthocenter (intersection of altitudes). Show your work in <think> </think> tags. Round the coordinates to 3 decimal places and return them inside parenthesis in <answer> </answer>, for example <answer> (0.304, 1.217) </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "(-29.000, -4.000)", "style": "rule" }
{ "index": 345, "split": "train" }
advanced_geometry/orthocenter
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nGiven triangle ABC with coordinates A=(1, 1), B=(-5, -8), and C=(4, -3), find the coordinates of its orthocenter. Show your work in <think> </think> tags. Round the coordinates to 3 decimal places and return them inside parenthesis in <answer> </answer>, for example <answer> (0.304, 1.217) </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "(2.765, -2.176)", "style": "rule" }
{ "index": 346, "split": "train" }
advanced_geometry/angle_measure
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nIn triangle ABC with coordinates A=(10, 1), B=(8, 3), and C=(7, -3), find the measure (in degrees) of angle ABC. Show your work in <think> </think> tags. Round the angle degrees to 2 decimal places, append a degree symbol, and return it in <answer> </answer> tags, for example <answer> 17.10° </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "54.46°", "style": "rule" }
{ "index": 347, "split": "train" }
advanced_geometry/angle_measure
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nGiven a triangle with vertices A=(8, -8), B=(6, 7), and C=(9, 6), determine the angle at B in degrees. Show your work in <think> </think> tags. Round the angle degrees to 2 decimal places, append a degree symbol, and return it in <answer> </answer> tags, for example <answer> 17.10° </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "63.97°", "style": "rule" }
{ "index": 348, "split": "train" }
advanced_geometry/orthocenter
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nGiven triangle ABC with coordinates A=(-5, 10), B=(-3, -6), and C=(-5, 5), find the coordinates of its orthocenter. Show your work in <think> </think> tags. Round the coordinates to 3 decimal places and return them inside parenthesis in <answer> </answer>, for example <answer> (0.304, 1.217) </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "(-93.000, -6.000)", "style": "rule" }
{ "index": 349, "split": "train" }
advanced_geometry/angle_measure
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nGiven a triangle with vertices A=(4, 4), B=(9, -4), and C=(5, -4), determine the angle at B in degrees. Show your work in <think> </think> tags. Round the angle degrees to 2 decimal places, append a degree symbol, and return it in <answer> </answer> tags, for example <answer> 17.10° </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "57.99°", "style": "rule" }
{ "index": 350, "split": "train" }
advanced_geometry/orthocenter
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nGiven triangle ABC with coordinates A=(0, -5), B=(-10, 3), and C=(4, 8), find the coordinates of its orthocenter. Show your work in <think> </think> tags. Round the coordinates to 3 decimal places and return them inside parenthesis in <answer> </answer>, for example <answer> (0.304, 1.217) </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "(-1.975, 0.531)", "style": "rule" }
{ "index": 351, "split": "train" }
advanced_geometry/incircle_radius
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nFind the incircle radius of triangle ABC whose vertices are A=(-3, 1), B=(-4, 5), and C=(-8, 0). Show your work in <think> </think> tags. Round the radius to 3 decimal places and return it in <answer> </answer> tags, for example <answer> 2.176 </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "1.344", "style": "rule" }
{ "index": 352, "split": "train" }
advanced_geometry/orthocenter
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nFor triangle with vertices A=(0, -10), B=(-6, 9), and C=(9, -7), determine the orthocenter (intersection of altitudes). Show your work in <think> </think> tags. Round the coordinates to 3 decimal places and return them inside parenthesis in <answer> </answer>, for example <answer> (0.304, 1.217) </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "(0.254, -9.762)", "style": "rule" }
{ "index": 353, "split": "train" }
advanced_geometry/incircle_radius
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nFind the incircle radius of triangle ABC whose vertices are A=(-2, 10), B=(-2, 7), and C=(-6, 1). Show your work in <think> </think> tags. Round the radius to 3 decimal places and return it in <answer> </answer> tags, for example <answer> 2.176 </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "0.598", "style": "rule" }
{ "index": 354, "split": "train" }
advanced_geometry/incircle_radius
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nConsider triangle ABC with coordinates A=(-8, 2), B=(4, -10), and C=(-2, 8). Compute the radius of its incircle. Show your work in <think> </think> tags. Round the radius to 3 decimal places and return it in <answer> </answer> tags, for example <answer> 2.176 </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "3.241", "style": "rule" }
{ "index": 355, "split": "train" }
advanced_geometry/orthocenter
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nGiven triangle ABC with coordinates A=(3, -3), B=(9, 4), and C=(1, 4), find the coordinates of its orthocenter. Show your work in <think> </think> tags. Round the coordinates to 3 decimal places and return them inside parenthesis in <answer> </answer>, for example <answer> (0.304, 1.217) </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "(3.000, 2.286)", "style": "rule" }
{ "index": 356, "split": "train" }
advanced_geometry/incircle_radius
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nConsider triangle ABC with coordinates A=(-5, 9), B=(-10, 9), and C=(-3, -7). Compute the radius of its incircle. Show your work in <think> </think> tags. Round the radius to 3 decimal places and return it in <answer> </answer> tags, for example <answer> 2.176 </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "2.073", "style": "rule" }
{ "index": 357, "split": "train" }
advanced_geometry/orthocenter
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nFor triangle with vertices A=(7, -2), B=(-8, 8), and C=(5, 4), determine the orthocenter (intersection of altitudes). Show your work in <think> </think> tags. Round the coordinates to 3 decimal places and return them inside parenthesis in <answer> </answer>, for example <answer> (0.304, 1.217) </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "(12.143, 14.714)", "style": "rule" }
{ "index": 358, "split": "train" }
advanced_geometry/orthocenter
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nFor triangle with vertices A=(-7, 3), B=(-2, 8), and C=(2, 5), determine the orthocenter (intersection of altitudes). Show your work in <think> </think> tags. Round the coordinates to 3 decimal places and return them inside parenthesis in <answer> </answer>, for example <answer> (0.304, 1.217) </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "(-2.286, 9.286)", "style": "rule" }
{ "index": 359, "split": "train" }
advanced_geometry/orthocenter
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nFor triangle with vertices A=(-7, 10), B=(3, 2), and C=(-1, 7), determine the orthocenter (intersection of altitudes). Show your work in <think> </think> tags. Round the coordinates to 3 decimal places and return them inside parenthesis in <answer> </answer>, for example <answer> (0.304, 1.217) </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "(16.333, 28.667)", "style": "rule" }
{ "index": 360, "split": "train" }
advanced_geometry/incircle_radius
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nConsider triangle ABC with coordinates A=(9, 0), B=(-9, -5), and C=(-2, 5). Compute the radius of its incircle. Show your work in <think> </think> tags. Round the radius to 3 decimal places and return it in <answer> </answer> tags, for example <answer> 2.176 </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "3.374", "style": "rule" }
{ "index": 361, "split": "train" }
advanced_geometry/incircle_radius
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nFind the incircle radius of triangle ABC whose vertices are A=(2, -10), B=(6, -8), and C=(9, -7). Show your work in <think> </think> tags. Round the radius to 3 decimal places and return it in <answer> </answer> tags, for example <answer> 2.176 </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "0.131", "style": "rule" }
{ "index": 362, "split": "train" }
advanced_geometry/incircle_radius
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nConsider triangle ABC with coordinates A=(-5, 4), B=(-7, 9), and C=(8, 7). Compute the radius of its incircle. Show your work in <think> </think> tags. Round the radius to 3 decimal places and return it in <answer> </answer> tags, for example <answer> 2.176 </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "2.097", "style": "rule" }
{ "index": 363, "split": "train" }
advanced_geometry/orthocenter
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nGiven triangle ABC with coordinates A=(3, 2), B=(8, -1), and C=(10, -7), find the coordinates of its orthocenter. Show your work in <think> </think> tags. Round the coordinates to 3 decimal places and return them inside parenthesis in <answer> </answer>, for example <answer> (0.304, 1.217) </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "(18.500, 7.167)", "style": "rule" }
{ "index": 364, "split": "train" }
advanced_geometry/angle_measure
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nGiven a triangle with vertices A=(-7, -1), B=(7, 2), and C=(1, 9), determine the angle at B in degrees. Show your work in <think> </think> tags. Round the angle degrees to 2 decimal places, append a degree symbol, and return it in <answer> </answer> tags, for example <answer> 17.10° </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "61.49°", "style": "rule" }
{ "index": 365, "split": "train" }
advanced_geometry/angle_measure
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nIn triangle ABC with coordinates A=(4, -2), B=(7, -3), and C=(8, 8), find the measure (in degrees) of angle ABC. Show your work in <think> </think> tags. Round the angle degrees to 2 decimal places, append a degree symbol, and return it in <answer> </answer> tags, for example <answer> 17.10° </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "76.76°", "style": "rule" }
{ "index": 366, "split": "train" }
advanced_geometry/angle_measure
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nIn triangle ABC with coordinates A=(7, 5), B=(-6, 7), and C=(3, 10), find the measure (in degrees) of angle ABC. Show your work in <think> </think> tags. Round the angle degrees to 2 decimal places, append a degree symbol, and return it in <answer> </answer> tags, for example <answer> 17.10° </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "27.18°", "style": "rule" }
{ "index": 367, "split": "train" }
advanced_geometry/incircle_radius
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nConsider triangle ABC with coordinates A=(-1, -10), B=(0, -8), and C=(-1, 4). Compute the radius of its incircle. Show your work in <think> </think> tags. Round the radius to 3 decimal places and return it in <answer> </answer> tags, for example <answer> 2.176 </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "0.495", "style": "rule" }
{ "index": 368, "split": "train" }
advanced_geometry/incircle_radius
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nFind the incircle radius of triangle ABC whose vertices are A=(-10, 0), B=(-4, 9), and C=(-4, -3). Show your work in <think> </think> tags. Round the radius to 3 decimal places and return it in <answer> </answer> tags, for example <answer> 2.176 </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "2.439", "style": "rule" }
{ "index": 369, "split": "train" }
advanced_geometry/orthocenter
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nGiven triangle ABC with coordinates A=(-9, -7), B=(-4, -7), and C=(-1, -4), find the coordinates of its orthocenter. Show your work in <think> </think> tags. Round the coordinates to 3 decimal places and return them inside parenthesis in <answer> </answer>, for example <answer> (0.304, 1.217) </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "(-1.000, -15.000)", "style": "rule" }
{ "index": 370, "split": "train" }
advanced_geometry/angle_measure
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nIn triangle ABC with coordinates A=(4, -5), B=(-8, 7), and C=(-1, -5), find the measure (in degrees) of angle ABC. Show your work in <think> </think> tags. Round the angle degrees to 2 decimal places, append a degree symbol, and return it in <answer> </answer> tags, for example <answer> 17.10° </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "14.74°", "style": "rule" }
{ "index": 371, "split": "train" }
advanced_geometry/orthocenter
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nGiven triangle ABC with coordinates A=(1, 9), B=(-3, 9), and C=(-2, -1), find the coordinates of its orthocenter. Show your work in <think> </think> tags. Round the coordinates to 3 decimal places and return them inside parenthesis in <answer> </answer>, for example <answer> (0.304, 1.217) </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "(-2.000, 8.700)", "style": "rule" }
{ "index": 372, "split": "train" }
advanced_geometry/orthocenter
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nGiven triangle ABC with coordinates A=(-3, -2), B=(-4, -4), and C=(7, -6), find the coordinates of its orthocenter. Show your work in <think> </think> tags. Round the coordinates to 3 decimal places and return them inside parenthesis in <answer> </answer>, for example <answer> (0.304, 1.217) </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "(-2.833, -1.083)", "style": "rule" }
{ "index": 373, "split": "train" }
advanced_geometry/orthocenter
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nFor triangle with vertices A=(-10, 6), B=(8, 9), and C=(8, -1), determine the orthocenter (intersection of altitudes). Show your work in <think> </think> tags. Round the coordinates to 3 decimal places and return them inside parenthesis in <answer> </answer>, for example <answer> (0.304, 1.217) </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "(6.833, 6.000)", "style": "rule" }
{ "index": 374, "split": "train" }
advanced_geometry/angle_measure
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nIn triangle ABC with coordinates A=(-8, -9), B=(2, -1), and C=(-9, 1), find the measure (in degrees) of angle ABC. Show your work in <think> </think> tags. Round the angle degrees to 2 decimal places, append a degree symbol, and return it in <answer> </answer> tags, for example <answer> 17.10° </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "48.96°", "style": "rule" }
{ "index": 375, "split": "train" }
advanced_geometry/orthocenter
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nGiven triangle ABC with coordinates A=(1, -7), B=(-1, -6), and C=(-2, 6), find the coordinates of its orthocenter. Show your work in <think> </think> tags. Round the coordinates to 3 decimal places and return them inside parenthesis in <answer> </answer>, for example <answer> (0.304, 1.217) </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "(-8.913, -7.826)", "style": "rule" }
{ "index": 376, "split": "train" }
advanced_geometry/angle_measure
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nIn triangle ABC with coordinates A=(-6, -6), B=(-1, 1), and C=(6, -8), find the measure (in degrees) of angle ABC. Show your work in <think> </think> tags. Round the angle degrees to 2 decimal places, append a degree symbol, and return it in <answer> </answer> tags, for example <answer> 17.10° </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "73.41°", "style": "rule" }
{ "index": 377, "split": "train" }
advanced_geometry/incircle_radius
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nFind the incircle radius of triangle ABC whose vertices are A=(1, -2), B=(2, -7), and C=(-7, -10). Show your work in <think> </think> tags. Round the radius to 3 decimal places and return it in <answer> </answer> tags, for example <answer> 2.176 </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "1.853", "style": "rule" }
{ "index": 378, "split": "train" }
advanced_geometry/angle_measure
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nGiven a triangle with vertices A=(9, 9), B=(-2, 5), and C=(5, -2), determine the angle at B in degrees. Show your work in <think> </think> tags. Round the angle degrees to 2 decimal places, append a degree symbol, and return it in <answer> </answer> tags, for example <answer> 17.10° </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "64.98°", "style": "rule" }
{ "index": 379, "split": "train" }
advanced_geometry/orthocenter
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nGiven triangle ABC with coordinates A=(-1, -10), B=(0, 6), and C=(9, -8), find the coordinates of its orthocenter. Show your work in <think> </think> tags. Round the coordinates to 3 decimal places and return them inside parenthesis in <answer> </answer>, for example <answer> (0.304, 1.217) </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "(2.722, -7.608)", "style": "rule" }
{ "index": 380, "split": "train" }
advanced_geometry/orthocenter
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nGiven triangle ABC with coordinates A=(-5, 7), B=(10, 8), and C=(6, 3), find the coordinates of its orthocenter. Show your work in <think> </think> tags. Round the coordinates to 3 decimal places and return them inside parenthesis in <answer> </answer>, for example <answer> (0.304, 1.217) </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "(6.338, -2.070)", "style": "rule" }
{ "index": 381, "split": "train" }
advanced_geometry/angle_measure
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nIn triangle ABC with coordinates A=(4, -6), B=(-9, 10), and C=(3, -8), find the measure (in degrees) of angle ABC. Show your work in <think> </think> tags. Round the angle degrees to 2 decimal places, append a degree symbol, and return it in <answer> </answer> tags, for example <answer> 17.10° </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "5.40°", "style": "rule" }
{ "index": 382, "split": "train" }
advanced_geometry/orthocenter
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nGiven triangle ABC with coordinates A=(-8, -5), B=(1, -9), and C=(9, 7), find the coordinates of its orthocenter. Show your work in <think> </think> tags. Round the coordinates to 3 decimal places and return them inside parenthesis in <answer> </answer>, for example <answer> (0.304, 1.217) </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "(1.545, -9.773)", "style": "rule" }
{ "index": 383, "split": "train" }
advanced_geometry/incircle_radius
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nFind the incircle radius of triangle ABC whose vertices are A=(0, 1), B=(-8, -4), and C=(-7, -1). Show your work in <think> </think> tags. Round the radius to 3 decimal places and return it in <answer> </answer> tags, for example <answer> 2.176 </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "0.956", "style": "rule" }
{ "index": 384, "split": "train" }
advanced_geometry/incircle_radius
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nConsider triangle ABC with coordinates A=(9, 5), B=(1, -9), and C=(-5, -1). Compute the radius of its incircle. Show your work in <think> </think> tags. Round the radius to 3 decimal places and return it in <answer> </answer> tags, for example <answer> 2.176 </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "3.579", "style": "rule" }
{ "index": 385, "split": "train" }
advanced_geometry/orthocenter
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nFor triangle with vertices A=(-9, 6), B=(4, -7), and C=(9, -2), determine the orthocenter (intersection of altitudes). Show your work in <think> </think> tags. Round the coordinates to 3 decimal places and return them inside parenthesis in <answer> </answer>, for example <answer> (0.304, 1.217) </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "(4.000, -7.000)", "style": "rule" }
{ "index": 386, "split": "train" }
advanced_geometry/angle_measure
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nGiven a triangle with vertices A=(-7, -10), B=(0, -10), and C=(-3, 5), determine the angle at B in degrees. Show your work in <think> </think> tags. Round the angle degrees to 2 decimal places, append a degree symbol, and return it in <answer> </answer> tags, for example <answer> 17.10° </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "78.69°", "style": "rule" }
{ "index": 387, "split": "train" }
advanced_geometry/orthocenter
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nFor triangle with vertices A=(-6, -10), B=(-6, -4), and C=(4, 0), determine the orthocenter (intersection of altitudes). Show your work in <think> </think> tags. Round the coordinates to 3 decimal places and return them inside parenthesis in <answer> </answer>, for example <answer> (0.304, 1.217) </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "(-10.000, 0.000)", "style": "rule" }
{ "index": 388, "split": "train" }
advanced_geometry/orthocenter
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nGiven triangle ABC with coordinates A=(-10, -9), B=(-10, 3), and C=(10, -5), find the coordinates of its orthocenter. Show your work in <think> </think> tags. Round the coordinates to 3 decimal places and return them inside parenthesis in <answer> </answer>, for example <answer> (0.304, 1.217) </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "(-8.400, -5.000)", "style": "rule" }
{ "index": 389, "split": "train" }
advanced_geometry/angle_measure
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nIn triangle ABC with coordinates A=(10, 5), B=(-8, 2), and C=(5, -5), find the measure (in degrees) of angle ABC. Show your work in <think> </think> tags. Round the angle degrees to 2 decimal places, append a degree symbol, and return it in <answer> </answer> tags, for example <answer> 17.10° </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "37.76°", "style": "rule" }
{ "index": 390, "split": "train" }
advanced_geometry/incircle_radius
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nFind the incircle radius of triangle ABC whose vertices are A=(5, -8), B=(-9, 5), and C=(9, 1). Show your work in <think> </think> tags. Round the radius to 3 decimal places and return it in <answer> </answer> tags, for example <answer> 2.176 </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "3.756", "style": "rule" }
{ "index": 391, "split": "train" }
advanced_geometry/orthocenter
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nGiven triangle ABC with coordinates A=(-8, 6), B=(-4, 2), and C=(6, -1), find the coordinates of its orthocenter. Show your work in <think> </think> tags. Round the coordinates to 3 decimal places and return them inside parenthesis in <answer> </answer>, for example <answer> (0.304, 1.217) </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "(-17.000, -24.000)", "style": "rule" }
{ "index": 392, "split": "train" }
advanced_geometry/incircle_radius
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nFind the incircle radius of triangle ABC whose vertices are A=(5, 0), B=(7, 7), and C=(-6, -8). Show your work in <think> </think> tags. Round the radius to 3 decimal places and return it in <answer> </answer> tags, for example <answer> 2.176 </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "1.498", "style": "rule" }
{ "index": 393, "split": "train" }
advanced_geometry/orthocenter
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nGiven triangle ABC with coordinates A=(5, 2), B=(-3, -5), and C=(1, -3), find the coordinates of its orthocenter. Show your work in <think> </think> tags. Round the coordinates to 3 decimal places and return them inside parenthesis in <answer> </answer>, for example <answer> (0.304, 1.217) </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "(16.167, -20.333)", "style": "rule" }
{ "index": 394, "split": "train" }
advanced_geometry/angle_measure
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nGiven a triangle with vertices A=(-1, -7), B=(-10, -6), and C=(-10, 8), determine the angle at B in degrees. Show your work in <think> </think> tags. Round the angle degrees to 2 decimal places, append a degree symbol, and return it in <answer> </answer> tags, for example <answer> 17.10° </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "96.34°", "style": "rule" }
{ "index": 395, "split": "train" }
advanced_geometry/incircle_radius
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nFind the incircle radius of triangle ABC whose vertices are A=(7, 8), B=(6, -8), and C=(-1, 7). Show your work in <think> </think> tags. Round the radius to 3 decimal places and return it in <answer> </answer> tags, for example <answer> 2.176 </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "3.125", "style": "rule" }
{ "index": 396, "split": "train" }
advanced_geometry/orthocenter
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nFor triangle with vertices A=(0, -1), B=(3, -2), and C=(6, 3), determine the orthocenter (intersection of altitudes). Show your work in <think> </think> tags. Round the coordinates to 3 decimal places and return them inside parenthesis in <answer> </answer>, for example <answer> (0.304, 1.217) </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "(3.889, -3.333)", "style": "rule" }
{ "index": 397, "split": "train" }
advanced_geometry/incircle_radius
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nConsider triangle ABC with coordinates A=(-8, -1), B=(-1, -3), and C=(-4, -4). Compute the radius of its incircle. Show your work in <think> </think> tags. Round the radius to 3 decimal places and return it in <answer> </answer> tags, for example <answer> 2.176 </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "0.842", "style": "rule" }
{ "index": 398, "split": "train" }
advanced_geometry/incircle_radius
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nFind the incircle radius of triangle ABC whose vertices are A=(2, 9), B=(-6, 5), and C=(-4, 4). Show your work in <think> </think> tags. Round the radius to 3 decimal places and return it in <answer> </answer> tags, for example <answer> 2.176 </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "0.843", "style": "rule" }
{ "index": 399, "split": "train" }