Question

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

Answer 1

The circumcenter is the center of the circle which goes through the three vertices of the triangle. Recall that all radii of a circle are congruent, i.e. equal to one another. So this is why the circumcenter is equidistant from the vertices of the triangle. 

Answer 2

The proof is explained in step-by-step explaination.

Explanation:

Circumcenter is the point at which the perpendicular bisector of sides of triangle intersects inside the circle.

This points lies inside the triangle as well as circle and the vertices of triangles lies on the circle. As a result the distance from circumcenter and vertices is called to be radius of the circle which is always equidistant from the center.

Hence, circumcenter is equidistant from the vertices of a triangle.