The centroid of the four points constituting an Orthocentric System is the center of the common Nine-Point Circle (Johnson 1929, p. 249). This fact automatically guarantees that the centroid of the Incenter and Excenters of a Triangle is located at the Circumcenter.

**References**

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

© 1996-9

1999-05-26