CAPS 2016 Problem 1

Let $P$ be a non-degenerate polygon with $n$ sides, where $n > 4$ . Prove that there exist three distinct vertices $A, B, C$ of $P$ 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)