1. The point that is equidistant from all three vertices of a triangle; the center of the circle that passes through all three vertices of a triangle.
Usage: geometry; mathematics

Examples

• The circumcenter of a right triangle lies on the hypotenuse.
• To find the circumcenter, construct the perpendicular bisectors of each side of the triangle.
• The circumcenter is equidistant from all three vertices of the triangle.
• In an acute triangle, the circumcenter lies inside the triangle.
• The circumcenter of an obtuse triangle is located outside the triangle.
• The circumradius is the distance from the circumcenter to any vertex.