Difference between revisions of "2001 JBMO Problems/Problem 4"
(Created page with "__TOC__ ==Problem== Let <math>N</math> 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...") |
(No difference)
|
Revision as of 00:51, 9 January 2023
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.
Soultion
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.
~ [AwesomeToad]