Question

what point is equidistant from all sides of a triangle? a. circumcenter b. incenter c. orthocenter d. centroid a city wants to place a bench in a triangular garden. they want the bench to be equidistant from all three corners of the garden. at what point should they place the bench? a. incenter b. circumcenter c. centroid d. orthocenter in an obtuse triangle, where is the circumcenter located? a. at the incenter b. at the centroid c. inside the triangle d. outside the triangle

Explanation:

1. The in - center of a triangle is the point of intersection of the angle bisectors and is equidistant from all sides of the triangle.
2. The circum - center of a triangle is the point of intersection of the perpendicular bisectors of the sides and is equidistant from all three vertices (corners) of the triangle.
3. In an obtuse - angled triangle, the circum - center is located outside the triangle.

Answer:

1. b. Incenter
2. b. Circumcenter
3. d. Outside the triangle