Excenter-Excenter Circle
Given a Triangle 
, the points 
, 
, and 
lie on a line, where is the Incenterand is the Excenter corresponding to . Furthermore, the circle with 
as the diameter has 
as itscenter, where 
is the intersection of 
with the Circumcircle of 
and is the point opposite on the Circumcircle. The circle with diameter also passes through 
and 
and has radius
It arises because the points
, , 
, and 
form an Orthocentric System.See also Excenter, Incenter-Excenter Circle, Orthocentric System
References
Johnson, R. A. Modern Geometry: An Elementary Treatise on the Geometry of the Triangle and the Circle. Boston, MA: Houghton Mifflin, pp. 185-186, 1929.
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