beautiful geometry proof

lark

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...e.php?id=27098

Laura

lark

I apparently can't edit that posting any more. But the link to the pdf with the other person's proof has changed, to http://www.artofproblemsolving.com/F...e.php?id=27177

Laura