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.
