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Euler line (Theorem)

In any triangle, the orthocenter $ H$, the centroid $ G$ and the circumcenter $ O$ are collinear, and $ OG/GH=1/2$. The line passing by these points is known as the Euler line of the triangle.


This line also passes by the center of the nine-point circle (or Feuerbach circle) $ N$, and $ N$ is the midpoint of $ OH$.

\includegraphics{eulin}



"Euler line" is owned by drini. [ full author list (2) | owner history (1) ]
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See Also: triangle, orthocenter, centroid, collinear, midpoint, orthic triangle, triangle center, Euler line proof


Attachments:
Euler line proof (Proof) by drini
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Cross-references: midpoint, nine-point circle, center, points, line, collinear, circumcenter, centroid, orthocenter, triangle
There are 3 references to this entry.

This is version 10 of Euler line, born on 2001-10-06, modified 2006-12-12.
Object id is 155, canonical name is EulerLine.
Accessed 10967 times total.

Classification:
AMS MSC: 51-00 (Geometry :: General reference works )
Pending Errata and Addenda
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