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ExcenterThe 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.See also Centroid (Orthocentric System), Excenter-Excenter Circle, ExcentralTriangle, Excircle, Incenter, 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.
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