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.

**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

1999-05-25