De Longchamp's Point

Date: 09/21/2000 at 14:15:29
From: Kevin Zencka
Subject: De Longchamp's point

What is De Longchamp's point, and how is it used?

Date: 09/24/2000 at 02:03:23
From: Doctor Floor
Subject: Re: De Longchamp's point

Hi, Kevin,

The De Longchamps point of a triangle is the reflection of the 
orthocenter through the circumcenter, a point on the Euler line. It is 
also the orthocenter of the anticomplementary triangle (formed by the 
lines through the vertices of a triangle parallel to the opposite 
sides).

It is named after De Longchamps, because he showed it is the radical 
center of the circles with the vertices of ABC as centers and the 
sidelengths of the opposite sides as radii.

For more on triangle centers, see Professor Clark Kimberling's 
(University of Evansville) Online Encyclopedia of Triangle Centers:

   http://cedar.evansville.edu/~ck6/encyclopedia/   

Best regards,
- Doctor Floor, The Math Forum
  http://mathforum.org/dr.math/