Which theorem explains why the circumcenter is equidistant from the vertices of a triangle a - vertical angles theorem b - concurrency of perpendicular bisectors theorem c - concurrency of angle bisector theorem d - alternate interior angles theorem

The answer is B. Remember the definition of the circumcenter of a triangle: the intersection of perpendicular bisectors. If we draw a perpendicular line to each of the three sides, these three lines intersect at a common point, and the distance of this point to all three vertices are equal, which can be proved using similar triangles. If we draw a circle with the circumcenter of the triangle as the center, and with the distance from circumcenter to vertices as the radius, the triangle will become inscribed in the circle.