Incenter-Excenter Circle
Given a triangle 
, the points 
, 
, and 
lie on a line, where is the Incenter and is the Excenter corresponding to . Furthermore, the Circle with 
as the Diameter has 
as its center, where is the intersection of 
with the Circumcircle of , and passes through
and 
. This Circle has Radius
It arises because
forms an Orthocentric System.See also Circumcircle, Excenter, Excenter-Excenter Circle, Incenter, Orthocentric System
References
Johnson, R. A. Modern Geometry: An Elementary Treatise on the Geometry of the Triangle and the Circle. Boston, MA: Houghton Mifflin, p. 185, 1929.
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