Question

Where do perpendicular bisectors of the sides of a triangle intersect?

A) At the centroid
B) At the orthocenter
C) At the incenter
D) At the circumcenter

Answer 1

The perpendicular bisectors of the sides of a triangle intersect at the circumcenter, which is the point equidistant from the triangle's vertices.

Step-by-step explanation:

The perpendicular bisectors of the sides of a triangle intersect at a specific point known as the circumcenter. This is the point that is equidistant from all the vertices of the triangle, and therefore, it is the center of the circumcircle that can be drawn around the triangle. Each perpendicular bisector is constructed by drawing a line that is perpendicular to a side of the triangle and that divides the side into two equal lengths. The circumcenter can be inside, on the edge, or outside the triangle depending on whether the triangle is acute, right, or obtuse.