Difference between revisions of "De Longchamps point"
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draw((0,0)--(44,60)--(44,-10)--cycle); | draw((0,0)--(44,60)--(44,-10)--cycle); | ||
Revision as of 12:35, 2 June 2008
- The title of this article has been capitalized due to technical restrictions. The correct title should be de Longchamps point.
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 point (  ) is the the orthocenter (  ) reflected through the circumcenter (  ).
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![[asy] draw((0,0)--(44,60)--(44,-10)--cycle); draw((0,0)--(44,0),blue+dashed); draw((44,60)--(22,-5),blue+dashed); draw((44,-10)--(6.5,10),blue+dashed); label("H",(24,0),(1,1)); dot((24,0)); draw((22,30)--(44,14),red); draw((22,-5)--(34,46),red); draw((44,25)--(18,25),red); dot((29,25)); label("C",(29,25),(1,1)); draw(Circle((29,25),25),dashed); dot((34,50)); label("L",(34,50),(1,1)); [/asy]](http://latex.artofproblemsolving.com/8/e/2/8e2fc3535addbb951f5f9621f4305542f0734745.png)
The de Longchamps point of a triangle is the reflection of the triangle's orthocenter through its circumcenter.
The point is collinear with the orthocenter and circumcenter.
