The Euler Line

The diagram below contains a triangle

$\Delta ABC$ with circumcentre

$O$ , centroid

$G$ and orthocentre

$H$ . Euler's theorem says that

$O$ ,

$G$ and

$H$ are collinear. You can see this in the diagram below; the Euler line through the points

$O$ ,

$G$ and

$H$ is coloured in black, and its extension is coloured in orange.

By moving the vertices

$A$ ,

$B$ and

$C$ you can see how the Euler line depends on these points.