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folding a transparent paper with 3 points to create an equilateral

Source: Sharygin Geometry Olympiad 2016 Final Round problem 5 grade 8

July 22, 2018
geometrypaperEquilateral Triangle

Problem Statement

Three points are marked on the transparent sheet of paper. Prove that the sheet can be folded along some line in such a way that these points form an equilateral triangle.
by A.Khachaturyan