de Longchamps point

From Wikipedia, the free encyclopedia

Jump to: navigation, search

The orthocenter H reflected about the circumcenter O gives the de Longchamps point L.

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 point is collinear with the orthocenter and circumcenter.^[1]

[edit] See also

^ ^a ^b Weisstein, Eric W. "de Longchamps Point." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/deLongchampsPoint.html

This geometry-related article is a stub. You can help Wikipedia by expanding it.