Assign to each side b of a convex polygon P the maximum area of a triangle that has b as a side and is contained in P. Show that the sum of the areas assigned to the sides of P is at least twice the area of P.(adsbygoogle = window.adsbygoogle || []).push({});

This was a 2006 Math olympiad question. A beautiful proof is at http://camoo.freeshell.org/IMO_2006_6.pdf" [Broken]. Two proofs there, actually.

The person who helped me complete the first proof made a pdf of his contribution, it's at http://artofproblemsolving.com/Forum/download/file.php?id=27098" [Broken]

Laura

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# Beautiful geometry proof

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