Circumcircle of a triangle + circumcenter

Dependencies: three points determine a circle (Three non-collinear points determine a unique circle).

Statement

Let $\triangle ABC$ be any triangle. Then there is a unique circle passing through the three vertices $A$, $B$, $C$, called the circumcircle of the triangle. Its center $O$ is called the circumcenter of $\triangle ABC$, and the radius $R = OA = OB = OC$ is called the circumradius:

The circumcenter $O$ is at the same time the common intersection of the three Perpendicular bisector ⇔ equidistant from endpointss of the sides $AB$, $BC$, $CA$ (see Three perpendicular bisectors meet (circumcenter)).