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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\nFind the incircle radius of triangle ABC whose vertices are A=(-6, 1), B=(-9, 0), and C=(-1, 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": "0.368", "style": "rule" }
{ "index": 1000, "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, 0), B=(5, -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": "73.74°", "style": "rule" }
{ "index": 1001, "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, 4), B=(4, 9), and C=(-9, -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": "0.702", "style": "rule" }
{ "index": 1002, "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=(4, 5), and C=(-7, 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": "3.55°", "style": "rule" }
{ "index": 1003, "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, 5), B=(-8, 1), 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": "(1.893, -7.793)", "style": "rule" }
{ "index": 1004, "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=(-2, 2), B=(-2, 4), 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": "0.719", "style": "rule" }
{ "index": 1005, "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, -9), and C=(-8, -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": "(-1.000, -4.500)", "style": "rule" }
{ "index": 1006, "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=(-9, -3), and C=(5, 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": "10.29°", "style": "rule" }
{ "index": 1007, "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, 3), B=(4, 1), and C=(-8, -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": "(-32.923, 53.308)", "style": "rule" }
{ "index": 1008, "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, -2), B=(5, 10), 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": "0.350", "style": "rule" }
{ "index": 1009, "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, -7), B=(0, -6), and C=(5, 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": "3.152", "style": "rule" }
{ "index": 1010, "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, 1), B=(10, -3), and C=(1, 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": "(-1.667, -3.000)", "style": "rule" }
{ "index": 1011, "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, -10), B=(9, 7), and C=(-3, -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": "3.773", "style": "rule" }
{ "index": 1012, "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=(8, 10), 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": "0.086", "style": "rule" }
{ "index": 1013, "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, 1), B=(-4, 1), and C=(5, 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": "0.310", "style": "rule" }
{ "index": 1014, "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=(3, 1), 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": "90.00°", "style": "rule" }
{ "index": 1015, "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, -7), 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": "(7.910, -5.917)", "style": "rule" }
{ "index": 1016, "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, 9), B=(-7, -3), and C=(8, -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": "3.412", "style": "rule" }
{ "index": 1017, "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=(-9, 10), and C=(-6, -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": "0.483", "style": "rule" }
{ "index": 1018, "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, 0), B=(-6, 2), and C=(1, 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": "53.97°", "style": "rule" }
{ "index": 1019, "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=(6, -8), 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": "0.812", "style": "rule" }
{ "index": 1020, "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=(2, 7), and C=(9, 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": "0.266", "style": "rule" }
{ "index": 1021, "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, -9), B=(1, 7), and C=(-4, 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": "2.265", "style": "rule" }
{ "index": 1022, "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=(-4, 9), and C=(-8, -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": "4.61°", "style": "rule" }
{ "index": 1023, "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, 4), B=(8, 2), and C=(6, 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": "(1.000, 2.000)", "style": "rule" }
{ "index": 1024, "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=(-5, -1), and C=(7, 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": "1.265", "style": "rule" }
{ "index": 1025, "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, 6), and C=(1, 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": "(0.545, 4.909)", "style": "rule" }
{ "index": 1026, "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=(6, 5), and C=(-8, -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": "(-4.645, 6.419)", "style": "rule" }
{ "index": 1027, "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, 5), B=(-10, 0), and C=(-6, -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": "(-13.857, -0.857)", "style": "rule" }
{ "index": 1028, "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=(6, -9), and C=(9, 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": "1.469", "style": "rule" }
{ "index": 1029, "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=(9, 10), and C=(2, -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": "(-32.286, 10.000)", "style": "rule" }
{ "index": 1030, "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, 1), B=(8, 10), and C=(-8, 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": "(-13.000, 17.000)", "style": "rule" }
{ "index": 1031, "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=(-5, -9), 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": "82.87°", "style": "rule" }
{ "index": 1032, "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, -4), B=(-9, 6), 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": "(-10.375, 7.000)", "style": "rule" }
{ "index": 1033, "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, -9), B=(5, 10), and C=(9, -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": "(11.192, -3.269)", "style": "rule" }
{ "index": 1034, "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, -3), B=(0, 1), and C=(4, -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": "111.04°", "style": "rule" }
{ "index": 1035, "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, 4), B=(2, -2), and C=(-9, -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": "2.382", "style": "rule" }
{ "index": 1036, "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, -9), B=(-5, 9), and C=(9, -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": "15.95°", "style": "rule" }
{ "index": 1037, "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, -6), and C=(2, -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": "(23.600, -85.000)", "style": "rule" }
{ "index": 1038, "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, 6), B=(9, -8), 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": "(34.385, 14.846)", "style": "rule" }
{ "index": 1039, "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, 7), B=(-9, 4), and C=(-2, -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": "3.061", "style": "rule" }
{ "index": 1040, "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, 5), B=(1, 0), and C=(-4, -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": "1.529", "style": "rule" }
{ "index": 1041, "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=(3, 5), and C=(-3, 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": "27.90°", "style": "rule" }
{ "index": 1042, "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, 9), B=(7, -1), and C=(8, -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": "153.84°", "style": "rule" }
{ "index": 1043, "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, 0), B=(5, -5), and C=(1, 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": "13.86°", "style": "rule" }
{ "index": 1044, "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, -1), B=(2, -4), and C=(0, -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": "0.242", "style": "rule" }
{ "index": 1045, "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, 5), B=(0, 3), and C=(-6, 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": "171.87°", "style": "rule" }
{ "index": 1046, "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, 6), B=(9, 2), and C=(4, 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": "(5.600, 2.000)", "style": "rule" }
{ "index": 1047, "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, 2), B=(1, -3), and C=(-8, 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": "(-21.077, -9.308)", "style": "rule" }
{ "index": 1048, "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, -2), B=(-9, 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": "(-12.889, 8.000)", "style": "rule" }
{ "index": 1049, "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, 5), B=(-2, -3), and C=(-6, -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": 1050, "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, 2), B=(1, -5), and C=(4, -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": "(-1.164, -4.098)", "style": "rule" }
{ "index": 1051, "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, 7), B=(1, 5), and C=(-9, 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": "167.47°", "style": "rule" }
{ "index": 1052, "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, -7), B=(-3, 9), and C=(3, 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": "2.509", "style": "rule" }
{ "index": 1053, "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=(3, 5), and C=(7, -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": "17.10°", "style": "rule" }
{ "index": 1054, "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=(3, 9), 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": "72.76°", "style": "rule" }
{ "index": 1055, "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=(-1, 8), and C=(7, 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": "0.924", "style": "rule" }
{ "index": 1056, "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=(-5, 5), 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": "(-14.500, -11.625)", "style": "rule" }
{ "index": 1057, "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, 6), B=(-6, -9), and C=(3, -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": "3.298", "style": "rule" }
{ "index": 1058, "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, 1), B=(-4, -5), and C=(-5, -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": "(-95.000, 99.000)", "style": "rule" }
{ "index": 1059, "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=(10, 9), and C=(6, 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": "2.73°", "style": "rule" }
{ "index": 1060, "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=(-6, 10), 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": "(2.387, 3.710)", "style": "rule" }
{ "index": 1061, "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, 0), B=(-7, -2), and C=(0, -8), 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": "(-2.200, -1.400)", "style": "rule" }
{ "index": 1062, "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=(6, -7), and C=(-10, -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": "1.866", "style": "rule" }
{ "index": 1063, "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, 0), B=(-9, 5), and C=(-4, 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": "(-4.068, 8.836)", "style": "rule" }
{ "index": 1064, "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, 3), B=(0, 6), and C=(-5, 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": "4.40°", "style": "rule" }
{ "index": 1065, "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, 10), B=(7, -1), and C=(4, 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": "2.205", "style": "rule" }
{ "index": 1066, "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=(10, -8), 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": "(8.342, 6.089)", "style": "rule" }
{ "index": 1067, "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, 10), B=(9, -8), and C=(-10, 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": "(-7.113, 4.085)", "style": "rule" }
{ "index": 1068, "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, 1), B=(10, -6), 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": "2.204", "style": "rule" }
{ "index": 1069, "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, -2), B=(6, -9), and C=(3, -8), 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": "(-36.000, -86.000)", "style": "rule" }
{ "index": 1070, "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, -4), B=(-8, 10), and C=(-7, -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": "0.842", "style": "rule" }
{ "index": 1071, "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=(4, 9), 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": "130.73°", "style": "rule" }
{ "index": 1072, "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, -9), B=(-9, -4), and C=(10, 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": "(1.409, -13.463)", "style": "rule" }
{ "index": 1073, "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=(6, -10), and C=(-7, -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": "54.46°", "style": "rule" }
{ "index": 1074, "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, -9), B=(-1, 0), and C=(2, 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": "(3.286, 2.143)", "style": "rule" }
{ "index": 1075, "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=(10, -9), and C=(-5, 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": "4.169", "style": "rule" }
{ "index": 1076, "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, 9), B=(-10, -1), and C=(-9, -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": "2.573", "style": "rule" }
{ "index": 1077, "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, 4), B=(-10, -10), and C=(-5, 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": "3.43°", "style": "rule" }
{ "index": 1078, "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, -3), B=(9, -9), and C=(-2, 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": "23.44°", "style": "rule" }
{ "index": 1079, "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, -9), B=(10, -2), and C=(0, 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": "(24.889, 5.444)", "style": "rule" }
{ "index": 1080, "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=(6, -10), and C=(6, -9), 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": "(44.857, 7.000)", "style": "rule" }
{ "index": 1081, "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, 6), B=(2, -5), and C=(-8, -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": "2.964", "style": "rule" }
{ "index": 1082, "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, 5), B=(8, -7), and C=(3, 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": "1.480", "style": "rule" }
{ "index": 1083, "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, -3), B=(-10, -2), and C=(-2, 8), 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": "(-7.643, -3.286)", "style": "rule" }
{ "index": 1084, "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, -2), B=(-7, -5), and C=(2, 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": "(-41.286, 22.429)", "style": "rule" }
{ "index": 1085, "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, -6), B=(3, -7), and C=(8, 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": "1.061", "style": "rule" }
{ "index": 1086, "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=(-4, 9), and C=(-9, -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": "64.61°", "style": "rule" }
{ "index": 1087, "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, 8), B=(5, -1), 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": "39.47°", "style": "rule" }
{ "index": 1088, "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=(1, 9), and C=(2, -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": "2.227", "style": "rule" }
{ "index": 1089, "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, -7), B=(0, 8), and C=(9, 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": "70.56°", "style": "rule" }
{ "index": 1090, "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, -2), B=(-4, 8), and C=(-6, 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": "(104.000, 98.000)", "style": "rule" }
{ "index": 1091, "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, -3), B=(1, 8), and C=(-5, -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": "3.876", "style": "rule" }
{ "index": 1092, "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, -6), B=(-4, 8), and C=(7, -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": "12.77°", "style": "rule" }
{ "index": 1093, "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=(1, 0), and C=(0, 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": "0.050", "style": "rule" }
{ "index": 1094, "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, -4), B=(-2, 4), and C=(-4, 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": "(-1.333, 5.333)", "style": "rule" }
{ "index": 1095, "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=(-1, 3), and C=(-6, 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": "(2.857, -13.714)", "style": "rule" }
{ "index": 1096, "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, -6), B=(-3, 8), and C=(-8, -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": "3.926", "style": "rule" }
{ "index": 1097, "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, -1), 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": "(-330.000, -561.000)", "style": "rule" }
{ "index": 1098, "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=(4, -8), and C=(4, -9), 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": "(4.200, -7.000)", "style": "rule" }
{ "index": 1099, "split": "train" }