De Longchamp's PointDate: 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/ |
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