Euler Line

The Circumcenter (C), Centroid (G) and Orthocenter (H) of a triangle all lie on a line called the Euler line of the triangle and HG=2GC.

Furthermore the center of the Ninepoint circle (N) also lies on the Euler line and is, indeed, the midpoint of CH.

Proof of the existence of the Euler line.

To play with a GSP sketch that shows the Euler line click here.