Here's a nice problem I found on math stack exchange (question 1182471).
ACE is a straight line and triangles ABC and CDE are equilateral. Prove that CP = CQ.
If you have a solution do put in the comments. I imagine there are a number of different solutions. I'll post mine this Monday coming.
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This is not a complete proof, but any proof is equivalent to prooving that CPQ is itself equilateral. This is because, the angles at the apex of CPQ are on a straight line and two lines of the triangle are equal. However, the final step eludes me.