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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}.

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