2001 JBMO Problems/Problem 4
Contents
[hide]Problem
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.
Solution
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.
2001 JBMO (Problems • Resources) | ||
Preceded by Problem 2 |
Followed by Last Question | |
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