This is from the "Azimuth" website of John Carlos Baez, a mathematician and physics professor at the University of California. He found it at Brian McCartin, Mysteries of the equilateral triangle.
Here is a sketch of the problem. My solution to follow in the Comments on 4 March.
Incidentally John Baez is the cousin of Joan Baez, a progressive and a famous folksinger. Her father, John's uncle, was a con-inventor of the electron microscope.
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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