Consider the excircles 
, 
, and 
of a triangle, and the external
Apollonius circle 
tangent externally to all
three. Denote the contact point of 
and 
by 
, etc. Then the lines 
, 
, and 
concur in a point known
as the Apollonius point, which has triangle
center function
![alpha=sin^2Acos^2[1/2(B-C)]](/images/equations/ApolloniusPoint/NumberedEquation1.svg) |
and is Kimberling center 
(Kimberling 1998, p. 102).
