## Excentral Triangle

The Triangle with Vertices corresponding to the Excenters of a given Triangle , also called the Tritangent Triangle.

Beginning with an arbitrary Triangle , find the excentral triangle . Then find the excentral triangle of that Triangle, and so on. Then the resulting Triangle approaches an Equilateral Triangle.

Call the Triangle tangent externally to the Excircles of . Then the Incenter of coincides with the Circumcenter of Triangle , where are the Excenters of . The Inradius of the Incircle of is

where is the Circumradius of , is the Inradius, and are the Exradii (Johnson 1929, p. 192).

See also Excenter, Excenter-Excenter Circle, Excircle, Mittenpunkt

References

Johnson, R. A. Modern Geometry: An Elementary Treatise on the Geometry of the Triangle and the Circle. Boston, MA: Houghton Mifflin, 1929.

© 1996-9 Eric W. Weisstein
1999-05-25