Using a Geogebra illustration, we prove the fundamental theorem of the Euler line: The Orthocenter (H), the Centroid (G), and the Circumcenter (O) of any triangle line on a straight line in that order, and the length HG is exactly double the length GO.
Proof writeup: https://colab.research.google.com/drive/1LMl5_YKUjvsBHzFsQwMdhU9djhJsJYs8?usp=sharing
Geogebra illustration: https://www.geogebra.org/geometry/yvmt8qrv
