messages listlengths 1 1 | ground_truth stringlengths 5 21 | dataset stringclasses 1 value | type stringclasses 1 value |
|---|---|---|---|
[
{
"content": "Given triangle ABC with coordinates A=(-2, -4), B=(10, -1), and C=(-7, -2), find the coordinates of its orthocenter. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | (-0.615, -27.538) | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(-4, -8), B=(7, 2), and C=(-5, 3), determine the orthocenter (intersection of altitudes). For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | (-3.244, 1.069) | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(5, 4), B=(1, -6), and C=(9, 9). Compute the radius of its incircle. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | 0.585 | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(1, -5), B=(7, 2), and C=(-1, 4), determine the angle at B in degrees. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | 63.43° | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(3, 5), B=(-2, -2), and C=(-6, -1), find the measure (in degrees) of angle ABC. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | 111.50° | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(1, 4), B=(4, 9), and C=(-9, -4), find the coordinates of its orthocenter. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | (36.000, -31.000) | Puzzle | advanced_geometry |
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(8, 9), B=(-8, -8), and C=(10, 5). For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | 1.959 | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(-5, 3), B=(-4, 8), and C=(5, 8), determine the angle at B in degrees. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | 101.31° | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(-7, -8), B=(-9, 6), and C=(-1, 4), find the coordinates of its orthocenter. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | (-4.111, 3.556) | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(-10, 2), B=(8, 10), and C=(10, -3), find the measure (in degrees) of angle ABC. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | 74.78° | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(5, 3), B=(-8, 5), and C=(-5, 9), determine the orthocenter (intersection of altitudes). For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | (-4.793, 10.345) | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(6, 7), B=(3, -7), and C=(-3, -1), find the coordinates of its orthocenter. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | (-2.176, -1.176) | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(-6, 10), B=(0, 0), and C=(-2, -10), determine the angle at B in degrees. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | 137.73° | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(-7, -9), B=(10, -3), and C=(4, -6). Compute the radius of its incircle. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | 0.415 | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(-5, 8), B=(9, 3), and C=(10, -9). Compute the radius of its incircle. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | 3.288 | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(5, 6), B=(9, 1), and C=(-3, 3). Compute the radius of its incircle. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | 1.918 | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(8, 1), B=(-10, -4), and C=(-9, -6). Compute the radius of its incircle. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | 1.043 | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(-4, -7), B=(-4, 0), and C=(-6, -2), find the coordinates of its orthocenter. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | (-9.000, -2.000) | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(2, 3), B=(-6, 8), and C=(-10, -4), determine the angle at B in degrees. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | 76.43° | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(-8, 10), B=(-8, -6), and C=(5, 8), determine the angle at B in degrees. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | 42.88° | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(2, 3), B=(8, 4), and C=(9, 1), find the measure (in degrees) of angle ABC. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | 98.97° | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(-4, 5), B=(9, -7), and C=(-2, -10), determine the orthocenter (intersection of altitudes). For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | (-0.386, -8.251) | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(10, 4), B=(-9, -8), and C=(2, 0), find the measure (in degrees) of angle ABC. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | 3.75° | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(1, 7), B=(3, -2), and C=(8, 0), determine the angle at B in degrees. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | 80.73° | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(-10, 10), B=(6, 3), and C=(-3, 9), find the coordinates of its orthocenter. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | (11.636, 42.455) | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(5, -4), B=(6, 0), and C=(-5, -2), determine the angle at B in degrees. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | 65.66° | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(-8, 8), B=(-7, 5), and C=(8, -10), determine the orthocenter (intersection of altitudes). For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | (-43.000, -27.000) | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(-8, -1), B=(-4, 3), and C=(-3, -8), determine the angle at B in degrees. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | 50.19° | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(-8, 5), B=(8, 10), and C=(0, -4). Compute the radius of its incircle. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | 4.095 | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(-10, 3), B=(10, -4), and C=(10, -8). Compute the radius of its incircle. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | 1.666 | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(1, 10), B=(10, 8), and C=(-2, 5), determine the angle at B in degrees. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | 26.57° | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(-10, 5), B=(10, 6), and C=(-1, 7), determine the angle at B in degrees. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | 8.06° | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(7, -2), B=(2, 7), and C=(8, -1), find the measure (in degrees) of angle ABC. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | 7.82° | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(-1, 10), B=(-10, -5), and C=(-8, 1), determine the angle at B in degrees. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | 12.53° | Puzzle | advanced_geometry |
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(-9, 1), B=(8, 1), and C=(-6, 4). For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | 1.434 | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(8, -7), B=(3, -6), and C=(-10, -5), find the measure (in degrees) of angle ABC. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | 173.09° | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(8, -1), B=(3, -2), and C=(-3, -2), determine the angle at B in degrees. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | 168.69° | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(5, 1), B=(0, 7), and C=(5, 4), find the coordinates of its orthocenter. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | (8.600, 7.000) | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(0, -5), B=(0, -3), and C=(-1, 7). Compute the radius of its incircle. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | 0.083 | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(1, 1), B=(-8, 9), and C=(-5, 8), determine the angle at B in degrees. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | 23.20° | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(-2, -7), B=(9, 1), and C=(-8, 5), find the measure (in degrees) of angle ABC. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | 49.27° | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(4, 2), B=(-2, -1), and C=(5, -6). Compute the radius of its incircle. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | 2.182 | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(-1, 10), B=(6, -4), and C=(3, -6), determine the orthocenter (intersection of altitudes). For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | (8.000, -3.500) | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(-10, 2), B=(1, 1), and C=(-10, 6), determine the orthocenter (intersection of altitudes). For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | (-10.455, 1.000) | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(-6, -8), B=(-3, -2), and C=(-3, -5), determine the angle at B in degrees. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | 26.57° | Puzzle | advanced_geometry |
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(6, 2), B=(0, 8), and C=(-10, 0). For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | 2.886 | Puzzle | advanced_geometry |
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(-9, 2), B=(-1, -7), and C=(10, 5). For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | 4.100 | Puzzle | advanced_geometry |
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(-2, 6), B=(8, -10), and C=(-4, 10). For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | 0.171 | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(10, 4), B=(-7, -8), and C=(1, -3), determine the angle at B in degrees. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | 3.21° | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(0, 4), B=(9, -10), and C=(5, 0). Compute the radius of its incircle. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | 1.005 | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(6, -8), B=(-6, -4), and C=(-2, -2). Compute the radius of its incircle. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | 1.475 | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(8, -7), B=(2, 5), and C=(-6, -10), determine the angle at B in degrees. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | 54.64° | Puzzle | advanced_geometry |
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(0, -4), B=(4, -10), and C=(-8, 1). For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | 0.850 | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(3, -5), B=(3, -6), and C=(0, 1), determine the angle at B in degrees. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | 23.20° | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(-5, -9), B=(5, -8), and C=(-3, -9), find the measure (in degrees) of angle ABC. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | 1.41° | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(-5, 5), B=(-8, 7), and C=(3, 0), find the measure (in degrees) of angle ABC. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | 1.22° | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(5, 5), B=(5, -9), and C=(6, 3). Compute the radius of its incircle. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | 0.495 | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(-8, -5), B=(8, -7), and C=(9, 9), determine the angle at B in degrees. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | 86.45° | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(-3, -4), B=(-8, 8), and C=(9, -2), determine the orthocenter (intersection of altitudes). For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | (-5.338, -7.974) | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(-9, -8), B=(4, -3), and C=(3, -2), determine the angle at B in degrees. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | 66.04° | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(10, 10), B=(-6, 6), and C=(-2, 0), determine the angle at B in degrees. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | 70.35° | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(3, -9), B=(9, 6), and C=(2, -7), find the measure (in degrees) of angle ABC. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | 6.50° | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(-1, 8), B=(-6, -9), and C=(-9, 7), determine the angle at B in degrees. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | 27.01° | Puzzle | advanced_geometry |
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(-3, -10), B=(-10, -8), and C=(-2, -6). For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | 1.527 | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(4, 7), B=(-1, 5), and C=(5, 2), find the coordinates of its orthocenter. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | (3.444, 5.889) | Puzzle | advanced_geometry |
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(4, 6), B=(2, -9), and C=(-9, -1). For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | 4.161 | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(7, -5), B=(-9, 1), and C=(-2, 8). Compute the radius of its incircle. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | 3.598 | Puzzle | advanced_geometry |
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(-1, 9), B=(-7, 8), and C=(5, -3). For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | 2.180 | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(-2, 9), B=(-10, 4), and C=(-1, -2). Compute the radius of its incircle. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | 2.972 | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(10, 6), B=(-10, 0), and C=(2, 9), determine the orthocenter (intersection of altitudes). For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | (-1.833, 21.778) | Puzzle | advanced_geometry |
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(-4, 8), B=(10, 0), and C=(5, -4). For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | 2.558 | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(-8, -4), B=(3, 2), and C=(5, 0), find the measure (in degrees) of angle ABC. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | 106.39° | Puzzle | advanced_geometry |
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(-6, -1), B=(0, 2), and C=(-3, 3). For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | 1.009 | Puzzle | advanced_geometry |
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(4, 6), B=(-8, 1), and C=(-5, 3). For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | 0.345 | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(10, 6), B=(-6, -6), and C=(9, 2). Compute the radius of its incircle. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | 1.264 | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(9, -1), B=(-7, 2), and C=(8, 3), find the measure (in degrees) of angle ABC. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | 14.43° | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(-7, -3), B=(4, -5), and C=(2, -9), find the coordinates of its orthocenter. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | (2.250, -7.625) | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(8, -6), B=(4, -4), and C=(7, -3), determine the orthocenter (intersection of altitudes). For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | (7.000, -3.000) | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(-10, -8), B=(9, -1), and C=(-4, 0), determine the orthocenter (intersection of altitudes). For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | (-8.455, 12.091) | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(5, -10), B=(0, 3), and C=(9, -4), determine the angle at B in degrees. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | 31.09° | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(9, -1), B=(7, 0), and C=(-9, 5), determine the orthocenter (intersection of altitudes). For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | (44.000, 111.000) | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(3, -7), B=(9, 2), and C=(-3, 1), determine the angle at B in degrees. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | 51.55° | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(3, -2), B=(5, -3), and C=(-3, 5), determine the orthocenter (intersection of altitudes). For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | (-16.000, -21.000) | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(-7, -5), B=(0, 8), and C=(6, -8), determine the angle at B in degrees. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | 48.86° | Puzzle | advanced_geometry |
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(6, 1), B=(-2, 8), and C=(-2, 6). For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | 0.725 | Puzzle | advanced_geometry |
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(-3, 10), B=(9, 2), and C=(-3, -4). For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | 4.015 | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(10, -2), B=(10, 0), and C=(-6, -10), determine the angle at B in degrees. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | 57.99° | Puzzle | advanced_geometry |
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(-7, 9), B=(9, -9), and C=(-8, -3). For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | 3.878 | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(4, -2), B=(-2, -10), and C=(-9, 7). Compute the radius of its incircle. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | 3.575 | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(-4, -1), B=(-10, -10), and C=(-4, 4), find the coordinates of its orthocenter. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | (17.000, -10.000) | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(-8, 3), B=(8, 2), and C=(-7, -9), determine the angle at B in degrees. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | 39.83° | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(6, 2), B=(-4, -3), and C=(-5, -7). Compute the radius of its incircle. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | 1.186 | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(4, 4), B=(-9, 1), and C=(-1, 9), determine the orthocenter (intersection of altitudes). For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | (-1.000, 9.000) | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(4, -8), B=(-8, 3), and C=(1, -5), find the measure (in degrees) of angle ABC. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | 0.88° | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(-1, -8), B=(9, -1), and C=(8, 6), determine the angle at B in degrees. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | 116.86° | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(-9, 5), B=(-4, -8), and C=(3, 9), determine the orthocenter (intersection of altitudes). For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | (-8.227, 4.682) | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(-1, 10), B=(1, -3), and C=(10, 0), determine the angle at B in degrees. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | 80.31° | Puzzle | advanced_geometry |
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(7, 7), B=(-1, 5), and C=(5, -9). For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | 3.131 | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(-6, 2), B=(2, 4), and C=(-10, 3), find the measure (in degrees) of angle ABC. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | 9.27° | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(3, -3), B=(-9, -4), and C=(-10, -3), determine the orthocenter (intersection of altitudes). For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | (-9.000, -15.000) | Puzzle | advanced_geometry |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.