|Jul1-10, 10:00 AM||#1|
beautiful geometry proof
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
|Jul5-10, 12:16 PM||#2|
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
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