ISL 1996 G9

In the plane, consider a point $X$ and a polygon $\mathcal{F}$ (which is not necessarily convex). Let $p$ denote the perimeter of $\mathcal{F}$ , let $d$ be the sum of the distances from the point $X$ to the vertices of $\mathcal{F}$ , and let $h$ be the sum of the distances from the point $X$ to the sidelines of $\mathcal{F}$ . Prove that $d^2 - h^2\geq\frac {p^2}{4}.$