Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Beautiful geometry proof

  1. Jul 1, 2010 #1
    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" [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]

    Last edited by a moderator: May 4, 2017
  2. jcsd
  3. Jul 5, 2010 #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/Forum/download/file.php?id=27177" [Broken]

    Last edited by a moderator: May 4, 2017
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook