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