A perpendicular bisector of a line segment is a line through the midpoint of the segment...

A perpendicular bisector of a line segment is a line through the midpoint of the segment, perpendicular to the segment (Figure 1.49). Prove that the perpendicular bisectors of the three sides of a triangle are concurrent. [Hint: Let K be the point of intersection of the perpendicular bisectors of .] The point K in Figure 1.50 is called the circumcenter of the triangle.