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de Longchamps point
In geometry, the de Longchamps point of a triangle is the reflection of its orthocenter about its circumcenter.[1] It is listed as X(20) in the Encyclopedia of Triangle Centers. Its trilinear coordinates are
\( \displaystyle\cos A - \cos B \cos C : \cos B - \cos C \cos A : \cos C - \cos A \cos B \)
The orthocenter H reflected about the circumcenter O gives the de Longchamps point L.
The point is collinear with the orthocenter and circumcenter.[1]
See also
Circumcircle
Excircle
Incircle
Notes
^ a b Weisstein, Eric W. "de Longchamps Point." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/deLongchampsPoint.html
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