excentral circle

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 J_A, J_B, and J_C. It also passes through Kimberling centers X_i for i = 1054, 1282, 1768, 2100, and 2101. It is a central circle with center at the Bevan point V and circumradius 2R, where R is the circumradius of the reference triangle. It has the extremely simple circle function l = 1 and the beautiful circle equation a(α + β)(α + γ) + b(α + β)(β + γ) + c(α + γ)(β + γ) = 0.

Bevan point | central circle | excenter | excentral triangle