The issue 7 of the Chalkdust mathematics magazine had an interesting geometric problem presented by Matthew Scroggs.
“In the diagram, ABDC is a square. Angles ACE and BDE are both 75°. Is triangle ABE equilateral? Why/why not?”
I had a solution, but alas, the Scroggs’s solution was far more elegant.
See the Chalkdust Triangle Problem for solutions.