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This is delightfully simple once you spot the way to do it, a real 'aha' question!
You are only given the three midpoints of the sides of a triangle. How can you construct the original triangle?
Prove that, given any three parallel lines, an equilateral triangle always exists with one vertex on each of the three lines.
Medieval stonemasons used a method to construct octagons using ruler and compasses... Is the octagon regular? Proof please.