The Euler Line
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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.