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2006 IMO Problems/Problem 6

Revision as of 23:15, 22 May 2014 by Swamih (talk | contribs) (Created page with "==Problem== Assign to each side <math>b</math> of a convex polygon <math>P</math> the maximum area of a triangle that has <math>b</math> as a side and is contained in <math>P</ma...")
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Problem

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 $P$.

Solution

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