For the benefit of those still in Christmas/New Year quiz mode, here is a simple mathematical problem: can you cut a line into 3 equal parts simply using a compass and a straight edge? This means no assumed angles (e.g. parallel, perpendicular) unless created by construction.
There are plenty of versions of how to solve this, but can you come up with one with a self evident proof which doesn't require any complicated trigonometric calculations to prove its correctness?
Hint, a proof using similar triangles in simple proportions would not be "complicated" for these purposes.
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