The diagram below contains a triangle $ΔABC$ 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.
See here.
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