The center J_i of an excircle. There are three excenters for a given triangle, denoted J_1, J_2, J_3. The incenter I and excenters J_i of a triangle are an orthocentric system.


where O is the circumcenter, J_i are the excenters, and R is the circumradius (Johnson 1929, p. 190). Denote the midpoints of the original triangle M_1, M_2, and M_3. Then the lines J_1M_1, J_2M_2, and J_3M_3 intersect in a point known as the mittenpunkt.

See also

Excenter-Excenter Circle, Excentral Triangle, Excircles, Incenter, Mittenpunkt, Orthocentric Centroid

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Coxeter, H. S. M. and Greitzer, S. L. Geometry Revisited. Washington, DC: Math. Assoc. Amer., p. 13, 1967.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.Wells, D. The Penguin Dictionary of Curious and Interesting Geometry. London: Penguin, pp. 115-116, 1991.

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Cite this as:

Weisstein, Eric W. "Excenter." From MathWorld--A Wolfram Web Resource.

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