# Euler line

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 $OH$.

 Title Euler line Canonical name EulerLine Date of creation 2013-03-22 11:44:25 Last modified on 2013-03-22 11:44:25 Owner drini (3) Last modified by drini (3) Numerical id 18 Author drini (3) Entry type Theorem Classification msc 51-00 Classification msc 58A05 Classification msc 83E15 Classification msc 83D05 Classification msc 83E05 Classification msc 83E50 Classification msc 81-00 Classification msc 83-00 Classification msc 82-00 Related topic Triangle Related topic Orthocenter Related topic Centroid Related topic Collinear Related topic Midpoint Related topic OrthicTriangle Related topic CenterOfATriangle Related topic EulerLineProof