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jamescai20
/
tts-reasoning

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2 values
reward_model
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=(5, -5), B=(8, -8), and C=(0, 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": "0.755", "style": "rule" }
{ "index": 800, "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, 6), B=(-10, 3), and C=(7, 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": "2.62°", "style": "rule" }
{ "index": 801, "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, 7), B=(-3, -7), and C=(9, 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": "4.13°", "style": "rule" }
{ "index": 802, "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=(-8, 7), and C=(-6, 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": "0.066", "style": "rule" }
{ "index": 803, "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, 5), B=(-5, -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": "1.231", "style": "rule" }
{ "index": 804, "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=(2, -5), B=(7, 8), and C=(-1, -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": "(23.207, -16.310)", "style": "rule" }
{ "index": 805, "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, -7), B=(-10, -1), 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": "(1.200, -3.400)", "style": "rule" }
{ "index": 806, "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, -1), B=(0, -10), 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": "1.027", "style": "rule" }
{ "index": 807, "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, -8), B=(6, 10), and C=(4, -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": "(-149.000, 10.000)", "style": "rule" }
{ "index": 808, "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, -1), B=(4, 3), 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": "145.30°", "style": "rule" }
{ "index": 809, "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=(-9, 3), B=(5, 4), and C=(1, 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": "55.43°", "style": "rule" }
{ "index": 810, "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=(1, 0), and C=(-7, -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": "(-41.000, 63.000)", "style": "rule" }
{ "index": 811, "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, 6), B=(7, 9), and C=(5, 9), 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": "(0.000, 20.667)", "style": "rule" }
{ "index": 812, "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, -5), B=(10, 7), and C=(-7, -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": "0.811", "style": "rule" }
{ "index": 813, "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, 7), B=(-9, 9), and C=(-6, -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": "2.205", "style": "rule" }
{ "index": 814, "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, -4), B=(5, 4), and C=(-3, 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, 2.500)", "style": "rule" }
{ "index": 815, "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, -8), B=(1, -5), 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": "30.96°", "style": "rule" }
{ "index": 816, "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=(-3, -7), B=(-8, 10), and C=(9, -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": "25.43°", "style": "rule" }
{ "index": 817, "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, -8), B=(-8, 7), and C=(1, 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": "3.338", "style": "rule" }
{ "index": 818, "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=(4, -9), B=(-10, -6), and C=(-6, 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": "(-7.776, -4.289)", "style": "rule" }
{ "index": 819, "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, 10), B=(6, -8), and C=(-6, -6), 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": "51.48°", "style": "rule" }
{ "index": 820, "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, 7), B=(3, 10), and C=(8, -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": "83.48°", "style": "rule" }
{ "index": 821, "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=(1, -4), and C=(-6, 10), 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": "(-159.000, -92.000)", "style": "rule" }
{ "index": 822, "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, 7), B=(-10, 4), and C=(10, -10), 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": "(6.641, 7.915)", "style": "rule" }
{ "index": 823, "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, -10), 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": "1.462", "style": "rule" }
{ "index": 824, "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, 4), B=(1, -4), and C=(9, 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": "0.960", "style": "rule" }
{ "index": 825, "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, 0), B=(7, 6), and C=(-10, -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": "(-23.500, 21.250)", "style": "rule" }
{ "index": 826, "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=(2, -3), B=(9, -3), and C=(4, 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": "(4.000, -2.000)", "style": "rule" }
{ "index": 827, "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, 4), B=(-9, 1), and C=(-1, 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": "2.522", "style": "rule" }
{ "index": 828, "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, -7), B=(4, -7), and C=(0, -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": "(0.000, -12.600)", "style": "rule" }
{ "index": 829, "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=(5, -6), B=(2, 3), and C=(5, 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": "130.60°", "style": "rule" }
{ "index": 830, "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=(8, -1), B=(10, 1), and C=(1, -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": "0.141", "style": "rule" }
{ "index": 831, "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=(-5, 1), B=(1, -10), and C=(-8, -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": "37.43°", "style": "rule" }
{ "index": 832, "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, 0), B=(3, 9), 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": "60.95°", "style": "rule" }
{ "index": 833, "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, -2), B=(4, 3), and C=(-9, -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": "20.58°", "style": "rule" }
{ "index": 834, "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=(3, -5), B=(5, -2), and C=(9, 9). 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": "0.327", "style": "rule" }
{ "index": 835, "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, -1), B=(0, 2), 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": "52.74°", "style": "rule" }
{ "index": 836, "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, 1), B=(-6, -10), and C=(-4, -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": "0.869", "style": "rule" }
{ "index": 837, "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=(-8, -2), B=(9, -4), 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": "1.004", "style": "rule" }
{ "index": 838, "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=(0, -5), B=(4, 10), 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": "58.37°", "style": "rule" }
{ "index": 839, "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=(-6, 10), and C=(10, 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": "2.657", "style": "rule" }
{ "index": 840, "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, -5), B=(0, 8), and C=(6, -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": "48.86°", "style": "rule" }
{ "index": 841, "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, 5), B=(-5, 9), and C=(7, -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": "87.06°", "style": "rule" }
{ "index": 842, "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, -9), B=(-1, 3), and C=(-8, 0), 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": "(-1.750, 2.083)", "style": "rule" }
{ "index": 843, "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, -7), and C=(-3, -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": "2.927", "style": "rule" }
{ "index": 844, "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=(2, 5), B=(-4, -4), and C=(1, 9), 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": "(13.818, 0.455)", "style": "rule" }
{ "index": 845, "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, 8), B=(4, 5), and C=(2, 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": "0.093", "style": "rule" }
{ "index": 846, "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=(9, -3), B=(9, -8), and C=(-5, 7), 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": "43.03°", "style": "rule" }
{ "index": 847, "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, -1), B=(-2, 6), and C=(-10, 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": "2.317", "style": "rule" }
{ "index": 848, "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, -2), B=(6, -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": "47.73°", "style": "rule" }
{ "index": 849, "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=(4, 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": "0.602", "style": "rule" }
{ "index": 850, "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, -4), B=(1, 4), 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": "57.43°", "style": "rule" }
{ "index": 851, "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=(5, -1), B=(1, -4), and C=(-9, 6), 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": "(0.000, -6.000)", "style": "rule" }
{ "index": 852, "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=(-10, 3), B=(-3, 7), and C=(-3, -3), 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": "60.26°", "style": "rule" }
{ "index": 853, "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, -7), B=(-5, 0), and C=(10, 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": "3.786", "style": "rule" }
{ "index": 854, "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, -2), B=(2, -2), 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": "2.235", "style": "rule" }
{ "index": 855, "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, -8), B=(0, -10), and C=(5, -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": "(1.538, -13.385)", "style": "rule" }
{ "index": 856, "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=(-8, 8), B=(-3, 0), 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": "1.912", "style": "rule" }
{ "index": 857, "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=(-3, 1), B=(-7, -8), and C=(-3, 0), 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": "2.60°", "style": "rule" }
{ "index": 858, "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=(-1, -7), B=(8, -6), 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": "(3.086, -4.771)", "style": "rule" }
{ "index": 859, "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, 10), B=(2, 5), and C=(-8, 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": "(3.757, -10.811)", "style": "rule" }
{ "index": 860, "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=(10, -8), B=(-1, 4), and C=(-5, 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": "0.353", "style": "rule" }
{ "index": 861, "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, -1), B=(6, 2), and C=(9, -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": "29.74°", "style": "rule" }
{ "index": 862, "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, 1), B=(7, 5), and C=(9, -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": "63.90°", "style": "rule" }
{ "index": 863, "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, 8), B=(1, -8), and C=(-2, -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": "0.821", "style": "rule" }
{ "index": 864, "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=(-6, -1), 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": "95.19°", "style": "rule" }
{ "index": 865, "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, 2), B=(-5, -9), and C=(-1, 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": "31.87°", "style": "rule" }
{ "index": 866, "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=(-4, -3), and C=(-10, 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": "3.771", "style": "rule" }
{ "index": 867, "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, 4), B=(10, -8), and C=(9, -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": "4.70°", "style": "rule" }
{ "index": 868, "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, 2), B=(-6, -5), 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": "(2.088, 1.471)", "style": "rule" }
{ "index": 869, "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, -4), B=(7, 3), and C=(10, -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": "69.37°", "style": "rule" }
{ "index": 870, "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, 5), B=(8, 0), and C=(0, 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": "0.107", "style": "rule" }
{ "index": 871, "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=(8, -5), and C=(0, -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": "0.758", "style": "rule" }
{ "index": 872, "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, 0), B=(5, -9), and C=(-2, 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": "0.323", "style": "rule" }
{ "index": 873, "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, -4), B=(6, -7), and C=(7, 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": "29.60°", "style": "rule" }
{ "index": 874, "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, -8), B=(-9, -8), 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": "40.10°", "style": "rule" }
{ "index": 875, "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=(10, 4), B=(-8, -6), and C=(1, -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": "53.02°", "style": "rule" }
{ "index": 876, "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=(-1, -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": "8.13°", "style": "rule" }
{ "index": 877, "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=(0, 3), B=(10, -6), and C=(0, -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": "36.28°", "style": "rule" }
{ "index": 878, "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, 2), B=(-8, 9), and C=(-5, -10), 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": "(4.800, 2.600)", "style": "rule" }
{ "index": 879, "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=(-4, -4), and C=(-8, -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": "1.365", "style": "rule" }
{ "index": 880, "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, 9), B=(1, 7), and C=(9, -10), 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": "(17.602, 20.107)", "style": "rule" }
{ "index": 881, "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=(0, 4), B=(-8, 2), and C=(10, -2), 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": "26.57°", "style": "rule" }
{ "index": 882, "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, -2), B=(2, -9), and C=(-1, -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": "0.458", "style": "rule" }
{ "index": 883, "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=(3, -6), B=(9, 1), and C=(-5, 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": "79.14°", "style": "rule" }
{ "index": 884, "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, -8), B=(-7, -4), and C=(-1, 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": "120.96°", "style": "rule" }
{ "index": 885, "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=(3, 7), B=(-6, -6), and C=(5, -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": "(5.897, -3.621)", "style": "rule" }
{ "index": 886, "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, -8), B=(-1, -8), and C=(9, 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": "2.401", "style": "rule" }
{ "index": 887, "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, 4), B=(-3, -2), and C=(5, -4), 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": "45.00°", "style": "rule" }
{ "index": 888, "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=(8, 4), and C=(-3, -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": "(1.524, 8.048)", "style": "rule" }
{ "index": 889, "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, 6), B=(10, 6), and C=(3, -6), 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": "59.74°", "style": "rule" }
{ "index": 890, "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, -5), B=(7, 6), and C=(-10, -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": "55.72°", "style": "rule" }
{ "index": 891, "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=(-3, -10), B=(-10, -8), and C=(-2, -6), 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": "(-3.067, -9.733)", "style": "rule" }
{ "index": 892, "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, 2), B=(-9, 0), and C=(-5, 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": "47.56°", "style": "rule" }
{ "index": 893, "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, -5), B=(-9, 9), and C=(-4, -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": "2.872", "style": "rule" }
{ "index": 894, "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, 10), B=(-8, 9), 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": "31.76°", "style": "rule" }
{ "index": 895, "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=(5, 1), B=(7, 10), and C=(-5, 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": "(8.295, -2.955)", "style": "rule" }
{ "index": 896, "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, -3), B=(-3, 0), 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": "0.815", "style": "rule" }
{ "index": 897, "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=(-2, -10), B=(-7, -1), 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": "(-7.095, -0.942)", "style": "rule" }
{ "index": 898, "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, 7), B=(2, 3), and C=(9, 0), 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": "(4.800, 4.200)", "style": "rule" }
{ "index": 899, "split": "train" }