Euler line

Revision as of 19:59, 4 November 2006 by JBL (talk | contribs) (Euler's line moved to Euler line: The line doesn't belong to Euler, it's named after him. "The Euler line of a triangle.")

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Let $ABC$ be a triangle, points $H, N, G, O, L$ as $\triangle ABC$'s orthocenter, nine-point center, centroid, circumcenter, De Longchamps point respectively, then these points are collinear(regardless of $\triangle ABC$'s shape). And the line passes through points $H, N, G, O, L$ is called as Euler line, which is named after Leonhard Euler.

An interesting property of distances between these points on the Euler line:

  • $OG:GN:NH\equiv2:1:3$
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