messages listlengths 1 1 | ground_truth stringlengths 5 21 | dataset stringclasses 1
value | type stringclasses 1
value |
|---|---|---|---|
[
{
"content": "In triangle ABC with coordinates A=(3, 1), B=(-4, 6), and C=(5, -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, coord... | 25.10° | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(8, -3), B=(9, 7), 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, o... | 19.49° | Puzzle | advanced_geometry |
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(-9, 5), B=(10, -1), 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 radi... | 1.508 | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(-1, -10), B=(-1, -6), and C=(-8, 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, coordinate... | 156.37° | Puzzle | advanced_geometry |
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(8, -4), B=(-10, 4), and C=(6, 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... | 4.136 | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(5, 9), B=(-4, -1), and C=(-9, -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,... | (-106.273, 78.545) | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(-8, -6), B=(-5, 8), and C=(-10, 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, coo... | (-13.062, 6.656) | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(-10, 8), B=(-2, 5), and C=(0, -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,... | (6.980, 10.612) | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(2, -5), B=(-8, 2), and C=(8, -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, coord... | (-482.000, -709.000) | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(4, 4), B=(-5, 2), and C=(1, 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, coordin... | (13.667, -54.000) | Puzzle | advanced_geometry |
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(3, 3), B=(6, 1), 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 a... | 0.223 | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(-1, 4), B=(3, -8), and C=(-7, 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, coor... | 10.62° | Puzzle | advanced_geometry |
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(-8, -6), B=(-3, -5), and C=(-9, 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 radi... | 1.964 | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(1, 3), B=(-1, 10), 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, coordi... | 37.18° | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(1, -3), B=(-4, -9), and C=(2, 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, ... | (25.633, -11.694) | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(7, -1), B=(-6, 3), 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, coordin... | 0.674 | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(-9, 10), B=(3, -7), 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, coordi... | 0.878 | Puzzle | advanced_geometry |
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(-3, 2), B=(6, 9), and C=(3, -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 ... | 2.599 | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(-4, -2), B=(4, -8), and C=(10, -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, coo... | 143.13° | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(10, -10), B=(-6, -6), and C=(2, -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, coor... | 0.483 | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(-9, -9), B=(2, -7), and C=(9, 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, o... | 141.49° | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(5, -3), B=(8, 1), and C=(7, -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... | 25.56° | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(-9, 6), B=(1, -6), and C=(-2, 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, coordin... | 1.068 | Puzzle | advanced_geometry |
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(-6, 3), B=(0, -9), and C=(-3, 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... | 1.876 | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(-3, 0), B=(2, 9), 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, coord... | 5.64° | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(8, 7), B=(0, 6), and C=(1, 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 r... | 83.09° | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(-10, 3), B=(-5, -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, coor... | 43.18° | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(1, -3), B=(-10, -7), and C=(-3, -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... | 35.93° | Puzzle | advanced_geometry |
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(2, 10), B=(0, 8), and C=(7, 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 ... | 0.662 | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(4, -10), B=(9, -2), and C=(-2, 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,... | (10.125, -1.578) | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(6, 2), B=(-5, 6), 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, coordina... | 2.603 | Puzzle | advanced_geometry |
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(-5, 4), B=(-1, 1), and C=(-9, -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 radiu... | 2.038 | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(8, 2), B=(-4, -6), and C=(-5, 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, coord... | (-1.195, 1.293) | Puzzle | advanced_geometry |
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(3, -2), B=(-10, -7), 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 radi... | 2.885 | Puzzle | advanced_geometry |
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(9, 2), B=(1, -5), 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... | 2.071 | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(2, -10), B=(9, 10), 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, coordi... | 1.300 | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(6, 6), B=(10, 9), and C=(7, -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, coordi... | (-1.860, 7.814) | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(-4, 5), B=(9, 4), and C=(7, 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, coordin... | (6.756, -2.171) | Puzzle | advanced_geometry |
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(4, -10), B=(-7, 8), 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 radiu... | 2.137 | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(-1, 8), B=(-9, -10), and C=(2, 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, ... | 16.27° | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(5, 5), B=(10, -4), and C=(7, -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, o... | 79.38° | Puzzle | advanced_geometry |
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(-2, 5), B=(4, -9), 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 ... | 2.603 | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(-8, 10), B=(10, -9), and C=(-6, 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, co... | 3.35° | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(-3, 7), B=(8, 10), and C=(6, -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, coor... | 69.03° | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(7, -3), B=(-1, -1), and C=(2, -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, coor... | (2.429, -5.286) | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(-4, 5), B=(3, -4), 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, c... | (-0.780, 4.505) | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(9, -1), B=(-9, -9), and C=(4, 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, ... | 31.66° | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(9, 5), B=(-3, 3), and C=(2, 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, coordinat... | 0.570 | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(0, 3), B=(-10, -1), and C=(0, 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, ... | (2.400, -1.000) | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(9, 4), B=(10, 1), 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... | 95.53° | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(0, -1), B=(-7, -6), and C=(2, -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, coor... | 6.48° | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(2, -9), B=(8, 8), and C=(-3, 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, coord... | (4.945, 7.196) | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(8, 4), B=(2, 8), and C=(-9, -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, coordin... | 3.020 | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(-7, -7), B=(-5, -1), 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, coor... | 1.529 | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(-2, 4), B=(-1, 10), and C=(7, 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, coordin... | 2.157 | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(-1, -5), B=(4, 9), and C=(-9, -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, coordi... | 2.165 | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(6, -8), B=(-5, 2), and C=(-7, 0), 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, coord... | (-4.619, 2.619) | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(-2, 9), B=(4, 2), 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, coordinat... | 1.479 | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(-6, 9), B=(-10, 3), and C=(8, 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, o... | 53.13° | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(6, -5), B=(0, -8), and C=(7, 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, coordi... | 38.42° | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(-10, 5), B=(8, 0), and C=(0, 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, c... | (-107.500, -385.000) | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(-4, 2), B=(-9, 7), and C=(-3, 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, o... | 18.43° | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(10, -8), B=(8, 8), 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, ... | (11.244, -8.220) | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(10, -6), B=(8, 0), and C=(-8, -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,... | (8.000, -0.667) | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(6, -7), B=(-8, -4), 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, coor... | 6.34° | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(4, 6), B=(-7, 9), and C=(8, -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... | 23.40° | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(6, -1), B=(2, 1), 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... | 160.56° | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(7, 1), B=(8, 8), and C=(-5, 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 ... | 50.26° | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(-5, -1), B=(10, -9), and C=(-3, -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, co... | (261.000, 493.000) | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(-2, 7), B=(-9, -8), and C=(2, -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, coordi... | 3.010 | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(3, 4), B=(-2, 9), and C=(2, -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... | 30.07° | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(5, -10), B=(0, 10), and C=(0, -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, coordi... | 1.427 | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(-2, 1), B=(1, -10), and C=(-2, -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,... | 21.61° | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(-7, 8), B=(-5, -8), and C=(-7, -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,... | 19.44° | Puzzle | advanced_geometry |
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(-1, -5), B=(-4, -2), and C=(-1, 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 radi... | 1.328 | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(3, 6), B=(-9, 3), and C=(5, -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... | 40.60° | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(-4, -2), B=(-4, -7), and C=(10, 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, coo... | (-7.571, 3.000) | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(1, -5), B=(-9, -2), and C=(9, -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, coor... | 4.17° | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(-2, 10), B=(6, 3), and C=(-4, 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, coord... | 46.90° | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(-9, 8), B=(-9, 4), and C=(6, -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, ... | (-18.333, -6.000) | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(7, 2), B=(6, -9), 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, coordinat... | 1.933 | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(9, 0), B=(-8, 3), and C=(4, -7), 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, c... | (4.224, -5.731) | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(1, -7), B=(-9, -4), and C=(-7, 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, coor... | 88.26° | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(7, 6), B=(-5, -1), and C=(-3, 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, coordin... | 0.358 | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(4, -9), B=(7, -7), 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, coordina... | 1.075 | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(8, -3), B=(-9, 7), and C=(-4, -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, coordi... | 2.081 | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(-2, -10), B=(-7, -1), and C=(9, 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, coord... | 3.799 | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(9, 5), B=(1, -9), and C=(-5, -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, coord... | (-1.595, -2.946) | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(-9, -2), B=(10, -4), and C=(-5, 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, coord... | 4.034 | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(-3, 7), B=(-6, -4), and C=(4, -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, ... | 63.43° | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(-3, -4), B=(1, 4), 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, coor... | 4.40° | Puzzle | advanced_geometry |
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(8, 1), B=(-1, 4), and C=(-10, -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 radiu... | 2.288 | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(4, -8), B=(1, -7), and C=(-10, -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, coo... | (4.000, 35.000) | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(1, 2), B=(6, 5), and C=(3, -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, coordin... | 40.60° | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(-9, -6), B=(7, 9), and C=(-5, -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, coor... | 11.63° | Puzzle | advanced_geometry |
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(-10, -8), B=(-5, -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 rad... | 1.135 | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(6, 0), B=(-8, 4), 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, coordina... | 3.295 | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(-9, 7), B=(0, -6), and C=(6, 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, c... | (1.667, -1.000) | Puzzle | advanced_geometry |
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(-6, -2), B=(9, -10), and C=(-5, 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 radi... | 3.169 | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(0, -5), B=(5, -2), and C=(2, 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, coordi... | (4.276, -1.793) | Puzzle | advanced_geometry |
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