## Excenter-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 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.

© 1996-9 Eric W. Weisstein
1999-05-25