Can the circumcenter of a triangle ABC ever be one of its ve

Can the circumcenter of a triangle ABC ever be one of its vertices? If no, prove it. If yes, state why.

Solution

No circumcentre can not be one of the vertices pf a triangle because The CIRCUMCENTER of a triangle is the point in the plane equidistant from the three vertices of the triangle. Since a point equidistant from two points lies on the perpendicular bisector of the segment determined by the two points, the circumcenter is the point of concurrency of the three perpendicular bisectors of each side of the triangle.