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A Quick Geometric Problem

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Michael Penn put this up on his YouTube channel earlier today, and it is indeed an elegant little problem. Here it is


Michael Penn solves this using congruent triangles, the angle sum of a triangle (180 °) and angles on a straight line (180 °). α is always 60 °, whatever the length of AD and CE. It's not that obvious and I was quite surprised.

However thinking about it later, I saw we can solve the problem using symmetry and the solution is super-nice. Here's how - just add a third line.



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