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.