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find so that exists n-gon if each diagonal is perp. bisector of another diagonal

Source: Iranian Geometry Olympiad 2018 IGO Advanced p3

September 19, 2018
geometrydiagonalperpendicularpolygon

Problem Statement

Find all possible values of integer n>3n > 3 such that there is a convex nn-gon in which, each diagonal is the perpendicular bisector of at least one other diagonal.
Proposed by Mahdi Etesamifard
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