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folding a square, perimeter question

Source: Nordic Mathematical Contest 1994 #3

October 4, 2017
geometry

Problem Statement

A piece of paper is the square ABCDABCD. We fold it by placing the vertex DD on the point D′D' of the side BCBC. We assume that ADAD moves on the segment A′D′A' D' and that A′D′A' D' intersects ABAB at EE. Prove that the perimeter of the triangle EBD′EBD' is one half of the perimeter of the square.
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