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

Answer 1

The theorem that explains why the circumcenter is equidistant from the vertices of a triangle is the Triangle Midsegment Theorem. This theorem states that the line segment connecting the midpoints of two sides of a triangle is parallel to the third side and is half as long as the third side. This means that the circumcenter, which is the point of intersection of the midsegments, is equidistant from the vertices of the triangle.