Definition:Euler Line

Definition
Let $\triangle ABC$ be a triangle which is not equilateral.

The Euler line of $\triangle ABC$ is the straight line through the orthocenter, centroid and circumcenter of $\triangle ABC$.


 * EulerLine.png

In the above, the line $OGK$ is the Euler line of $\triangle ABC$.

Also see

 * Centroid of Triangle divides Line from Circumcenter to Orthocenter in 2 to 1 Ratio
 * Centroid, Circumcenter and Orthocenter of Equilateral Triangle are Same Point