2001 JBMO Problems/Problem 4
Contents
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.
See also
2001 JBMO (Problems • Resources) | ||
Preceded by Problem 2 |
Followed by Last Question | |
1 • 2 • 3 • 4 | ||
All JBMO Problems and Solutions |