messages listlengths 1 1 | ground_truth stringlengths 5 21 | dataset stringclasses 1 value | type stringclasses 1 value |
|---|---|---|---|
[
{
"content": "Given a triangle with vertices A=(-6, -10), B=(-3, -4), and C=(-10, -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"
}
] | 47.49° | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(6, 0), B=(7, 10), and C=(-10, -10), 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"
}
] | (21.467, -13.147) | Puzzle | advanced_geometry |
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(8, 7), B=(-7, -1), 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"
}
] | 0.815 | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(-3, 10), B=(-10, 8), and C=(4, 6), 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"
}
] | (-1.048, 23.667) | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(1, -9), B=(-3, 2), and C=(8, -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"
}
] | 3.060 | Puzzle | advanced_geometry |
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(-2, 7), B=(5, -10), 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"
}
] | 1.191 | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(-4, 4), B=(6, 5), and C=(6, 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"
}
] | 84.29° | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(-6, 6), B=(4, -8), and C=(-7, 4), 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"
}
] | 6.97° | Puzzle | advanced_geometry |
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(3, -3), B=(-5, 2), and C=(-4, -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"
}
] | 0.956 | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(-10, 1), B=(-8, 0), and C=(-6, 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"
}
] | 108.43° | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(8, 0), B=(6, 9), and C=(-4, 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"
}
] | 91.22° | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(7, 10), B=(3, -8), 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"
}
] | 84.09° | Puzzle | advanced_geometry |
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(-6, 4), B=(4, 9), and C=(-10, 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"
}
] | 2.216 | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(5, -3), B=(-7, -7), and C=(1, 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"
}
] | 3.284 | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(6, -9), B=(-4, -7), and C=(6, 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"
}
] | (3.600, -7.000) | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(-10, 9), B=(2, 9), 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"
}
] | 135.00° | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(3, -6), B=(9, 1), and C=(-5, 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"
}
] | 79.14° | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(9, 10), B=(4, 1), and C=(-8, 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"
}
] | (6.492, -5.051) | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(-10, 2), B=(-4, 5), and C=(-3, -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"
}
] | 68.63° | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(5, -10), B=(7, -2), and C=(-7, 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"
}
] | 84.09° | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(-4, -6), B=(-1, 2), and C=(4, 1), 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"
}
] | (-2.140, 3.302) | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(7, 6), B=(2, 4), and C=(8, -4), 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"
}
] | 74.93° | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(-7, -6), B=(9, -1), 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"
}
] | 41.32° | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(-4, 4), B=(6, 10), and C=(1, 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"
}
] | (2.080, 0.200) | Puzzle | advanced_geometry |
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(-3, 6), B=(0, 8), and C=(-5, 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"
}
] | 0.625 | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(5, -7), B=(-10, 8), and C=(-6, 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"
}
] | 6.34° | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(6, -7), B=(7, 9), and C=(7, 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"
}
] | (279.000, -7.000) | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(-5, -4), B=(-7, -9), and C=(-3, 2), 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"
}
] | 1.82° | Puzzle | advanced_geometry |
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(-2, -7), B=(-7, 0), and C=(6, -7). 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"
}
] | 1.785 | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(-6, -5), B=(-9, 2), and C=(7, 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"
}
] | 84.16° | Puzzle | advanced_geometry |
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(10, 10), B=(5, 7), and C=(-5, -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"
}
] | 1.088 | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(6, -2), B=(-9, 2), and C=(10, -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"
}
] | 0.19° | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(-6, 0), B=(1, -7), and C=(-8, -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"
}
] | 1.216 | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(-1, -1), B=(-5, -8), and C=(-6, -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"
}
] | 0.159 | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(9, 0), B=(5, 4), 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"
}
] | 45.00° | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(9, 4), B=(10, -8), and C=(9, -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"
}
] | 4.70° | Puzzle | advanced_geometry |
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(-9, 6), B=(1, 9), and C=(4, 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"
}
] | 2.005 | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(4, 1), B=(6, 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"
}
] | 104.04° | Puzzle | advanced_geometry |
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(2, -3), B=(2, 9), and C=(-6, 2). 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"
}
] | 2.994 | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(2, 9), B=(-7, 1), and C=(-4, -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"
}
] | 2.143 | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(5, -1), B=(-8, 7), and C=(-1, 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"
}
] | 2.081 | Puzzle | advanced_geometry |
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(-7, -5), B=(3, -4), 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"
}
] | 2.877 | Puzzle | advanced_geometry |
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(-5, -6), B=(-1, 1), and C=(-6, -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"
}
] | 1.456 | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(9, 5), B=(7, -2), and C=(-4, -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"
}
] | 138.42° | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(-1, -4), B=(6, 7), and C=(-9, -10), 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"
}
] | 8.95° | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(0, 5), B=(8, -10), and C=(-6, -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"
}
] | 35.36° | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(-2, -9), B=(-3, -5), and C=(8, -3), 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"
}
] | (-2.609, -5.652) | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(8, 9), B=(4, -5), and C=(-5, -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"
}
] | 105.95° | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(4, 8), B=(-5, -1), and C=(1, 2), 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"
}
] | 18.43° | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(4, -10), B=(-10, 1), and C=(5, -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"
}
] | 10.08° | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(3, 1), B=(3, 3), and C=(6, -5), 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"
}
] | (-13.000, -5.000) | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(2, -8), B=(1, -6), and C=(10, -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"
}
] | 39.47° | Puzzle | advanced_geometry |
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(-3, -7), B=(-1, -5), and C=(-10, 8). 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"
}
] | 1.250 | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(7, 1), B=(3, -2), and C=(1, -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"
}
] | 140.91° | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(-3, -3), B=(10, 1), and C=(9, 5). 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"
}
] | 1.742 | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(-10, 5), B=(-8, 6), and C=(5, -5), 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"
}
] | (-3.714, 12.429) | Puzzle | advanced_geometry |
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(-5, 9), B=(-3, -5), and C=(-2, -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"
}
] | 0.766 | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(7, 4), B=(2, 4), and C=(7, -8), 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"
}
] | 67.38° | Puzzle | advanced_geometry |
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(2, 7), B=(8, 4), and C=(-3, -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"
}
] | 2.232 | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(4, 0), B=(1, -5), and C=(1, -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"
}
] | 149.04° | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(-7, 9), B=(-1, -6), and C=(-10, -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"
}
] | 3.398 | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(-9, -3), B=(-7, 2), and C=(10, 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"
}
] | (-7.809, 7.124) | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(0, -4), B=(9, -2), and C=(-2, -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"
}
] | 19.94° | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(-6, 0), B=(-1, 9), and C=(5, -6), 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"
}
] | 50.86° | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(8, -7), B=(3, -6), and C=(-6, 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"
}
] | 157.62° | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(2, 10), B=(0, 3), and C=(-1, -4), 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"
}
] | 172.18° | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(10, 5), B=(-1, -5), and C=(7, 10). 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"
}
] | 2.255 | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(6, -10), B=(9, 2), and C=(3, 10). 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"
}
] | 2.254 | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(10, 10), B=(9, 2), and C=(6, 2), 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"
}
] | 97.13° | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(-5, 8), B=(-6, 7), and C=(-2, 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"
}
] | 71.57° | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(-5, 8), B=(-4, -3), and C=(3, -8), 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"
}
] | (-17.778, -9.889) | Puzzle | advanced_geometry |
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(-6, -9), B=(9, 8), and C=(3, -7). 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"
}
] | 2.560 | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(-5, -2), B=(-10, -6), and C=(-6, -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"
}
] | 1.533 | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(-10, 9), B=(-1, -9), and C=(1, -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"
}
] | 71.57° | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(3, 1), B=(5, -10), and C=(7, -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"
}
] | 24.34° | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(2, 3), B=(-8, -9), 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"
}
] | 1.996 | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(-7, -2), B=(-6, -4), and C=(4, 6), 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"
}
] | (-8.667, -0.333) | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(-5, 2), B=(10, 3), and C=(-4, -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"
}
] | 12.13° | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(-8, -6), B=(-10, -7), and C=(8, -7), 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"
}
] | (-8.000, 25.000) | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(-3, -9), B=(3, 5), and C=(-7, 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"
}
] | 3.690 | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(2, -9), B=(1, 4), and C=(-1, 8), 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"
}
] | (42.727, 11.364) | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(1, -6), B=(-4, -4), and C=(-7, 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"
}
] | (-13.308, -10.769) | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(2, 5), B=(9, 10), and C=(6, -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"
}
] | 39.21° | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(-6, -2), B=(3, -7), and C=(7, 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"
}
] | (2.644, -5.842) | Puzzle | advanced_geometry |
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(-9, 2), B=(2, 3), and C=(3, -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"
}
] | 2.697 | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(6, 5), B=(-7, 3), and C=(3, 4), 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"
}
] | (11.857, -53.571) | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(-6, 4), B=(-6, -2), 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"
}
] | (-4.250, -3.000) | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(-8, -1), B=(-1, -3), 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"
}
] | (-5.385, -8.846) | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(2, -4), B=(3, -5), and C=(5, -1). 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"
}
] | 0.592 | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(-8, 4), B=(3, -2), and C=(8, 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"
}
] | 2.642 | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(10, -9), B=(5, 1), 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"
}
] | 153.43° | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(-8, 8), B=(-6, 1), and C=(2, -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"
}
] | 126.50° | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(1, -8), B=(4, -3), 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"
}
] | 0.996 | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(-3, 9), B=(-4, -8), and C=(8, -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"
}
] | 4.187 | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(4, -10), B=(0, -3), 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"
}
] | 138.18° | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(-10, 7), B=(-2, 1), 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"
}
] | 1.497 | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(10, -4), B=(4, 2), and C=(10, -1). 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"
}
] | 0.989 | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(-7, -5), B=(-4, 6), and C=(-4, -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"
}
] | (-18.667, -5.000) | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(-7, -4), B=(-6, -4), and C=(2, 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"
}
] | 0.367 | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(0, 10), B=(1, 6), and C=(7, -4), 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"
}
] | 163.07° | Puzzle | advanced_geometry |
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