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Combinatorial geometry gem

Source: Kvant Magazine No. 11-12 2023 M2777

March 16, 2024
combinatorial geometryhomothetycombinatoricsgeometry

Problem Statement

A convex polygon P\mathcal{P} with a center of symmetry OO{} is drawn in the plane. Prove that it is possible to place a rhombus in P\mathcal{P} whose image following a homothety of factor two centered at OO contains P\mathcal{P}.
Proposed by I. Bogdanov, S. Gerdzhikov and N. Nikolov
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