2001 JBMO Problems/Problem 4
Let be a convex polygon with 1415 vertices and perimeter 2001. Prove that we can find 3 vertices of N which form a triangle of area smaller than 1.
The largest side has length at least . Therefore, the sum of the other sides is . Divide these sides into pairs of adjacent sides, and there exist one pair of sides such that . Blah blah blah... we know how to prove except why would a problem want you to do that.... no idea.
Well, then and the area of the triangle with sides and the angle between them has area as desired.
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