Euler line

Revision as of 11:57, 6 July 2007 by JBL (talk | contribs)

In any triangle $\triangle ABC$, the Euler line is a line which passes through the orthocenter $H$, centroid $G$, circumcenter $O$, nine-point center $N$ and De Longchamps point $L$. It is named after Leonhard Euler. Its existence is a non-trivial theorem of Euclidean geometry.


An image is supposed to go here. You can help us out by creating one and editing it in. Thanks.


Certain fixed orders and distance ratios hold among these points. In particular, $\overline{OGNH}$ and $OG:GN:NH = 2:1:3$


Given the orthic triangle$\triangle H_AH_BH_C$ of $\triangle ABC$, the Euler lines of $\triangle AH_BH_C$,$\triangle BH_CH_A$, and $\triangle CH_AH_B$ concur at $N$, the nine-point center of $\triangle ABC$.


This article is a stub. Help us out by expanding it.

Invalid username
Login to AoPS