Three perpendicular bisectors meet (circumcenter)

Dependencies: perpendicular bisector = locus of equidistant points (Perpendicular bisector ⇔ equidistant from endpoints) and its converse (Perpendicular bisector test).

Statement

Let $\triangle ABC$ be any triangle. Then the three Perpendicular bisector ⇔ equidistant from endpointss of the sides $AB$, $BC$, $CA$ meet at a single point $P$, called the circumcenter of the triangle. This point also satisfies