IMO Shortlist 2004 problem G6


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2. travnja 2012.
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Let P be a convex polygon. Prove that there exists a convex hexagon that is contained in P and whose area is at least \frac34 of the area of the polygon P.

Alternative version. Let P be a convex polygon with n\geq 6 vertices. Prove that there exists a convex hexagon with

a) vertices on the sides of the polygon (or)
b) vertices among the vertices of the polygon

such that the area of the hexagon is at least \frac{3}{4} of the area of the polygon.

I couldn't solve this one, partially because I'm not quite sure of the statements' meaning (a) or (b) :)
Obviously if a) is true then so is b).
Izvor: Međunarodna matematička olimpijada, shortlist 2004