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diagonal of inscribed KLMN in square ABCD is // to side of ABCD having 1/2 area

Source: Iranian Geometry Olympiad 2021 IGO Elementary p2

January 25, 2022
inscribedgeometryareassquare

Problem Statement

Points K,L,M,NK, L, M, N lie on the sides AB,BC,CD,DAAB, BC, CD, DA of a square ABCDABCD, respectively, such that the area of KLMNKLMN is equal to one half of the area of ABCDABCD. Prove that some diagonal of KLMNKLMN is parallel to some side of ABCDABCD.
Proposed by Josef Tkadlec - Czech Republic
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