The Bevan circle, sometimes also called the excentral circle, is the circumcircle of the excentral triangle of the reference triangle, i.e., it is the circle passing through the excenters , , and . It also passes through Kimberling centers for , 1282, 1768, 2100, and 2101.
It is a central circle with center at the Bevan point and circumradius , where is the circumradius of the reference triangle. It has the extremely simple circle function
and the beautiful circle equation
It is orthogonal to the Stevanović circle.