Which is the only center point that lies on the edge of a triangle?

The circumcenter is the point where a triangle’s perpendicular bisectors meet. In a right triangle, it lies at the midpoint of the hypotenuse, which is an edge of the triangle. An incenter lies inside the triangle, and the circumcenter of an obtuse triangle lies outside it. Therefore, the circumcenter of a right triangle is the only listed point on an edge.

AI-written and checked against the verified answer.