IMO 2009 Shortlist G5

Let P be a polygon that is convex and symmetric to some point O. Prove that for some parallelogram R satisfying P ⊂ R we...

imomathematicsolympiadshortlistgeometry

IMO 2009 Shortlist G5

Category: Geometry

Problem

Let P be a polygon that is convex and symmetric to some point O. Prove that for some parallelogram R satisfying P ⊂ R we have |R| |P| ≤ √ where |R| and |P| denote the area of the sets R and P, respectively.