Question 182
Let $P$ be a non-degenerate polygon with $n$ sides, where $n \gt 4$. Prove that there exist three distinct vertices $A, B, C$ of $P$ with the following property: if $l_1, l_2, l_3$ 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 $l_1, l_2$ and $l_3$.