The center of an Excircle. There are three excenters for a given Triangle, denoted , ,
. The Incenter and excenters of a Triangle are an Orthocentric System.

where is the Circumcenter, are the excenters, and is the Circumradius (Johnson 1929, p. 190). Denote the Midpoints of the original Triangle , , and . Then the lines , , and intersect in a point known as the Mittenpunkt.

**References**

Dixon, R. *Mathographics.* New York: Dover, pp. 58-59, 1991.

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

© 1996-9

1999-05-25