de Longchamps point

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]

See also

• Circumcircle
• Excircle
• Incircle

Notes

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

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