MathDB

Let

P

be a non-degenerate polygon with

n

sides, where

n > 4

. Prove that there exist three distinct vertices

A, B, C

P

with the following property:If

\ell_1,\ell_2,\ell_3

are the lengths of the three polygonal chains into which

A, B, C

break the perimeter of

P

, then there is a triangle with side lengths

\ell_1,\ell_2

and

\ell_3

. Remark: By a non-degenerate polygon we mean a polygon in which every two sides are disjoint, apart from consecutive ones, which share only the common endpoint.(Poland)

Problem Statement