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restore the original paper rectangle using compass and ruler

Source: Sharygin 2011 Final 8.2

December 13, 2018
geometryrectangleconstructionpaper

Problem Statement

Peter made a paper rectangle, put it on an identical rectangle and pasted both rectangles along their perimeters. Then he cut the upper rectangle along one of its diagonals and along the perpendiculars to this diagonal from two remaining vertices. After this he turned back the obtained triangles in such a way that they, along with the lower rectangle form a new rectangle. Let this new rectangle be given. Restore the original rectangle using compass and ruler.