Neuberg’s Theorem

https://commons.wikimedia.org/wiki/File:Neuberg_6.gif
Image: Wikimedia Commons

Construct squares outwardly on the sides of triangle ABC, and make a triangle of their centers. Now the centers of squares constructed inwardly on the sides of that triangle will fall on the midpoints of the sides of ABC.

(Due to Luxembourger mathematician Joseph Neuberg, 1840-1926.)

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