Viviani's Theorem (TANTON Mathematics)

Pick a point inside an equilateral triangle and sum its three distances to each of the sides of the triangle. Then this sum has value the height of the triangle, no matter the point initially chosen.

This charmer is attributed to 17th-century mathematician Viviani. Here we prove the result, and then go further and let the point wander outside the triangle, and then go to shapes other than triangles!

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• VivianiTheorem