A park has the shape of a convex pentagon of area . A man standing at an interior point of the park notices that he stands at a distance of at most from each vertex of the pentagon. Prove that he stands at a distance of at least from each side of the pentagon.
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$(YUG 2)$ A park has the shape of a convex pentagon of area $50000\sqrt{3} m^2$. A man standing at an interior point $O$ of the park notices that he stands at a distance of at most $200 m$ from each vertex of the pentagon. Prove that he stands at a distance of at least $100 m$ from each side of the pentagon.
Izvor: Međunarodna matematička olimpijada, shortlist 1969
Školjka 
A park has the shape of a convex pentagon of area 
. A man standing at an interior point 
of the park notices that he stands at a distance of at most 
from each vertex of the pentagon. Prove that he stands at a distance of at least 
from each side of the pentagon.