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lark
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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.
This was a 2006 Math olympiad question. A beautiful proof is at http://camoo.freeshell.org/IMO_2006_6.pdf" . 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"
Laura
This was a 2006 Math olympiad question. A beautiful proof is at http://camoo.freeshell.org/IMO_2006_6.pdf" . 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"
Laura
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