Question 18
G9 (UKR) In the plane are given a point $O$ and a polygon $\mathcal F$ (not necessarily convex). Let $P$ denote the perimeter of $\mathcal F$, $D$ the sum of the distances from $O$ to the vertices of $\mathcal F$, and $H$ the sum of the distances from $O$ to the lines containing the sides of $\mathcal F$. Prove that
$$D^2-H^2\ge\frac{P^2}4.$$
$$D^2-H^2\ge\frac{P^2}4.$$