Question

Which theorem explains why the circumcenter is equidistant from the vertices of a triangle?

Answer 1

As per the problem, we have been asked to find the name of the theorem which explains why the circum-center is equidistant from the vertices of a triangle

A.Vertical Angles Theorem:

The vertical angle theorem is about the angles formed when two straight lines cut each other. Hence this is not the correct option

B.Concurrency of Perpendicular Bisectors Theorem

Perpendicular bisectors passing through the same point called the circum-center of the triangle. The point of intersection is always equidistant from the endpoints.

Hence theorem "B.Concurrency of Perpendicular Bisectors Theorem" explains why the circumcenter is equidistant from the vertices of a triangle.

C. Concurrency of Angle Bisector Theorem:

This gives you the incenter of the triangle.

D. Alternate Interior Angles Theorem

This theorem states that if two parallel lines are intersected by a line then the alternate interior angles are congruent.