MathDB
IMO Shortlist 2009 - Problem G5

Source:

July 5, 2010
geometryparallelogramgeometric inequalityareapolygonIMO Shortlist

Problem Statement

Let PP be a polygon that is convex and symmetric to some point OO. Prove that for some parallelogram RR satisfying P⊂RP\subset R we have ∣R∣∣P∣≤2\frac{|R|}{|P|}\leq \sqrt 2 where ∣R∣|R| and ∣P∣|P| denote the area of the sets RR and PP, respectively.
Proposed by Witold Szczechla, Poland
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