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
See also Excenter, Excenter-Excenter Circle, Excircle, Mittenpunkt
Johnson, R. A. Modern Geometry: An Elementary Treatise on the Geometry of the Triangle and the Circle. Boston, MA:
Houghton Mifflin, 1929.