The perpendicular bisectors of the sides of a triangle are concurrent.

Proof

Let P be the center of the circumcircle of triangle ABC, and let M be the midpoint of side AC. AC is a chord of circle P and PM is a line through the center of the circle that bisects AC. Hence PM is perpendicular to AC. (A line through the center of a circle that bisects a chord in perpendicular to the chord). Therefore PM is the perpendicular bisector of AC and so is the perpendicular bisectors of the sides of a triangle are concurrent.