messages listlengths 1 1 | ground_truth stringlengths 5 21 | dataset stringclasses 1
value | type stringclasses 1
value |
|---|---|---|---|
[
{
"content": "Consider triangle ABC with coordinates A=(-10, 1), B=(8, 10), 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, coordi... | 2.106 | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(-9, -2), B=(-9, 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, coordin... | 1.259 | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(6, 10), B=(1, 4), and C=(-9, 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, coordi... | (1.650, -0.875) | Puzzle | advanced_geometry |
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(-8, 8), B=(5, 2), 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 radius... | 2.217 | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(-3, 10), B=(-9, 5), and C=(-3, -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, coo... | 84.81° | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(-9, -6), B=(-4, 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, coo... | 28.41° | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(9, -9), B=(5, 9), 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... | 7.45° | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(-7, -1), B=(-4, 2), and C=(-9, 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, ... | 56.31° | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(5, -4), B=(2, 1), and C=(-10, -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, ... | 94.40° | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(-8, 6), B=(-4, 2), and C=(6, -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... | 0.882 | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(-9, 1), B=(6, -2), and C=(0, 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... | 33.69° | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(3, -10), B=(-8, -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,... | 41.93° | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(9, -10), B=(-6, 2), and C=(0, -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, ... | 17.65° | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(9, -10), B=(-5, -10), and C=(-8, 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 angl... | (-8.000, -15.100) | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(-9, -9), B=(7, 3), and C=(0, -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, ... | (7.000, -18.333) | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(-6, -10), B=(8, 6), and C=(4, 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... | 0.188 | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(-10, 7), B=(-4, 10), 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, coor... | (-1.692, 17.385) | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(2, -4), B=(-3, -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, coordi... | 0.053 | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(3, 3), B=(8, -9), 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, coordi... | (12.857, 12.857) | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(10, -7), B=(5, -1), 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, coordinates,... | 170.04° | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(0, 3), B=(-7, 9), and C=(4, 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... | 2.212 | Puzzle | advanced_geometry |
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(-7, -2), B=(-3, 9), and C=(0, 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... | 2.423 | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(0, 0), B=(-7, -5), and C=(9, 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, coordi... | 3.53° | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(7, 10), B=(-1, 5), and C=(-6, 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, coord... | (37.889, -67.222) | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(-4, 8), B=(-3, -7), and C=(2, -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,... | (3.154, -3.923) | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(8, -7), B=(5, 3), 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, coordi... | (9.536, 8.361) | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(-6, 5), B=(-10, -5), 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, coor... | 0.807 | Puzzle | advanced_geometry |
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(10, -1), B=(5, -7), and C=(0, -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 radiu... | 0.995 | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(2, 6), B=(0, 6), and C=(-4, -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... | 105.95° | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(-3, 3), B=(-10, -3), 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, co... | 62.98° | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(-10, 0), B=(-4, 9), and C=(-8, 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... | 1.294 | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(0, 3), B=(-1, 1), 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, c... | (-1.000, 1.000) | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(4, -7), B=(-6, -3), and C=(5, -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,... | (4.059, -6.353) | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(-10, -2), B=(5, -4), and C=(-8, -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, co... | 16.34° | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(6, 3), B=(2, -9), and C=(-2, 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, c... | (-1.286, -0.238) | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(10, -10), B=(4, -1), 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, coo... | 145.49° | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(-2, -5), B=(-6, -10), and C=(-6, 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, co... | (1.500, -5.000) | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(8, -9), B=(3, -9), and C=(1, 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... | 2.142 | Puzzle | advanced_geometry |
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(-7, 0), B=(-8, 5), and C=(2, -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... | 1.103 | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(-2, 4), B=(10, -3), and C=(-1, 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, ... | 14.74° | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(-3, -4), B=(-7, -9), and C=(7, -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... | (-8.870, 9.696) | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(-2, -3), B=(7, 1), and C=(0, -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, coord... | 21.04° | Puzzle | advanced_geometry |
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(1, -7), B=(2, -3), 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 radiu... | 1.508 | Puzzle | advanced_geometry |
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(6, -4), B=(-2, 9), and C=(-4, 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... | 2.190 | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(2, 5), B=(9, 10), 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... | 0.633 | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(-7, -4), B=(6, 6), and C=(9, 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, coordi... | (105.667, -116.667) | Puzzle | advanced_geometry |
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(9, 3), B=(6, 7), and C=(4, -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 a... | 1.644 | Puzzle | advanced_geometry |
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(5, -4), B=(4, -7), and C=(0, -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... | 1.137 | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(1, 0), B=(-9, -5), 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, coord... | 8.97° | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(6, -10), B=(3, 4), and C=(1, -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, coord... | (-2.062, -8.656) | Puzzle | advanced_geometry |
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(-4, 5), B=(-4, -2), and C=(-7, -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 radi... | 1.245 | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(8, -7), B=(1, 2), 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, c... | (-7.500, -12.167) | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(9, -7), B=(0, -4), 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, ... | (-8.905, -13.714) | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(-5, -9), B=(-8, 5), and C=(10, -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,... | 59.47° | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(-4, -6), B=(3, -7), 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,... | (3.429, -6.000) | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(5, -6), B=(-9, -6), and C=(7, -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, ... | 7.13° | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(-1, 0), B=(-5, 4), and C=(-6, -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,... | (2.714, -0.286) | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(-5, 5), B=(5, -2), and C=(-2, -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,... | (0.758, -3.061) | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(0, -5), B=(6, 2), 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, coord... | (5.049, -2.756) | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(-1, -3), B=(0, 2), and C=(-5, 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... | (-1.957, -0.609) | Puzzle | advanced_geometry |
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(-1, -8), B=(4, -1), and C=(3, 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... | 0.633 | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(-7, 6), B=(-2, 2), and C=(6, 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, coordi... | (-1.463, -0.328) | Puzzle | advanced_geometry |
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(-1, -5), B=(9, 2), and C=(3, 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 ... | 2.974 | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(-10, -8), B=(-3, 8), 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, co... | (4.431, -5.376) | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(1, 0), B=(-1, 5), and C=(-10, -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... | 61.09° | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(4, -10), B=(-9, -9), and C=(5, 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, coor... | 45.00° | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(5, -4), B=(10, 8), and C=(4, 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... | 48.95° | Puzzle | advanced_geometry |
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(0, -4), B=(-3, -4), and C=(-7, -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 radi... | 0.576 | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(3, -10), B=(-5, 8), and C=(4, -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, coor... | 15.33° | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(-5, 4), B=(3, -8), and C=(-1, -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, coor... | (-1.643, -9.429) | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(-4, 9), B=(-1, -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, ... | 31.81° | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(4, -4), B=(7, 4), 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, coordi... | (-9.588, -1.529) | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(-7, -7), B=(7, 4), 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, o... | 18.15° | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(-6, 8), B=(-9, 4), and C=(0, -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... | 86.82° | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(9, -3), B=(7, -8), and C=(3, 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... | 41.78° | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(-3, -2), B=(-7, 7), and C=(-9, 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,... | (-3.000, 9.667) | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(5, -3), B=(-3, -5), and C=(-10, 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... | 100.98° | Puzzle | advanced_geometry |
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(-10, 6), B=(-2, -1), 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 radiu... | 2.431 | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(1, -5), B=(-6, 6), and C=(10, 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, coord... | (1.278, -0.550) | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(5, 5), B=(4, 1), and C=(-4, -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, c... | (19.840, -11.960) | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(6, 8), B=(7, -6), and C=(-2, -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... | 56.86° | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(7, 9), B=(8, -10), and C=(4, 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, coordi... | 11.02° | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(-7, -1), B=(6, -4), and C=(0, -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, coor... | (-3.677, -20.935) | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(4, 1), B=(3, -9), and C=(-4, -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,... | (5.710, -10.971) | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(-5, -6), B=(9, 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, coord... | (9.000, -11.000) | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(9, -7), B=(3, 5), and C=(-8, -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, ... | (3.944, -3.028) | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(5, -9), B=(-6, 1), and C=(9, 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, coordi... | (4.116, -2.372) | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(-7, -1), B=(2, 2), 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, c... | (5.000, -1.000) | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(-3, 1), B=(-4, 5), and C=(-8, 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, ... | (-3.238, 1.190) | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(1, 3), B=(-8, 2), and C=(10, -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, coordin... | 2.170 | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(2, -4), B=(-8, 5), and C=(9, 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, coordi... | 55.23° | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(5, -6), B=(2, 3), 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, coordin... | 130.60° | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(5, -9), B=(-10, 7), 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... | (9.778, 2.605) | Puzzle | advanced_geometry |
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(7, 8), B=(-7, -5), and C=(0, -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... | 2.227 | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(1, -9), B=(8, -1), 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, coordi... | (10.328, -1.537) | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(-2, -2), B=(-5, 0), and C=(4, -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, ... | 7.94° | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(-2, 10), B=(-8, -7), 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, coordi... | 3.881 | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(-2, 2), B=(-7, -1), and C=(5, 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, ... | (-46.000, 90.000) | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(-10, -6), B=(-3, 6), 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, coor... | 0.358 | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(-10, -1), B=(-10, 6), and C=(10, -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, coordinate... | 68.20° | Puzzle | advanced_geometry |
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