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.

**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.

© 1996-9

1999-05-26