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A regular nonagon and four equilateral triangles. The purple and yellow triangles share a vertex. Prove that the yellow triangles also share a vertex.

Scroll down for a solution to this problem.


Solution by Matthew Arcus.

A proof by construction: if the short dashed lines are the same length, then we have two congruent isosceles triangles so the equal sides of the yellow triangle are at 60°. The purple triangles just have to be isosceles for this to work.

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