Question 70
(YUG 2) A park has the shape of a convex pentagon of area $5\sqrt3$ ha ($=50000\sqrt3\ \mathrm{m}^2$). A man standing at an interior point $O$ of the park notices that he stands at a distance of at most $200\ \mathrm m$ from each vertex of the pentagon. Prove that he stands at a distance of at least $100\ \mathrm m$ from each side of the pentagon.