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.
- Elongated Orthobirotunda
- Elongated Orthocupolarotunda
- Elongated Pentagonal Cupola
- Elongated Pentagonal Dipyramid
- Elongated Pentagonal Gyrobicupola
- Elongated Pentagonal Gyrobirotunda
- Elongated Pentagonal Gyrocupolarotunda
- Elongated Pentagonal Orthobicupola
- Elongated Pentagonal Orthobirotunda
- Elongated Pentagonal Orthocupolarotunda
- Elongated Pentagonal Pyramid
- Elongated Pentagonal Rotunda
- Elongated Pyramid
- Elongated Rotunda
- Elongated Square Cupola
- Elongated Square Dipyramid
- Elongated Square Gyrobicupola
- Elongated Square Pyramid
- Elongated Triangular Cupola
- Elongated Triangular Dipyramid
- Elongated Triangular Gyrobicupola
- Elongated Triangular Orthobicupola
- Elongated Triangular Pyramid
- Elsasser Function
- Wilson's Primality Test