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.
See also
Excenter-Excenter Circle,
Excentral Triangle,
Excircles,
Incenter,
Mittenpunkt,
Orthocentric Centroid
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References
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.Referenced on Wolfram|Alpha
Excenter
Cite this as:
Weisstein, Eric W. "Excenter." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Excenter.html
Subject classifications
