Question

The perpendicular bisectors of a triangle are concurrent. Their common point is the: A. centroid B. incenter C. circumcenter D. orthocenter

Answer 1

The common point where the perpendicular bisectors of a triangle converge is called the circumcenter, which is the point from which a circumcircle can be drawn around the triangle. Therefore correct option is C

Step-by-step explanation:

The perpendicular bisectors of a triangle are concurrent, meaning they all meet at a single point. This common point is known as the circumcenter of the triangle. It is not the centroid, incenter, or orthocenter. The circumcenter is equidistant from all three vertices of the triangle and is the point from which you can draw a circle, called the circumcircle, that perfectly encircles the triangle.

All three perpendicular bisectors of a triangle are indeed perpendicular to their respective sides and they bisect these sides, which means that the circumcenter can lie inside, on, or outside the triangle depending on the type of triangle (acute, right, or obtuse).