Bevan 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


and the beautiful circle equation


It is orthogonal to the Stevanović circle.

See also

Bevan Point, Central Circle, Excenter, Excentral Triangle

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Kimberling, C. "Clark Kimberling's Encyclopedia of Triangle Centers--ETC."

Referenced on Wolfram|Alpha

Bevan Circle

Cite this as:

Weisstein, Eric W. "Bevan Circle." From MathWorld--A Wolfram Web Resource.

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