IMO Shortlist 1969 problem 70
Dodao/la:
arhiva2. travnja 2012. ![(YUG 2)](/media/m/7/8/1/781abb0e686611f084fe576a56d6287d.png)
A park has the shape of a convex pentagon of area
![50000\sqrt{3} m^2](/media/m/c/e/a/cea88504105cb35a48cacf5d7f3d2d0b.png)
. A man standing at an interior point
![O](/media/m/9/6/0/9601b72f603fa5d15addab9937462949.png)
of the park notices that he stands at a distance of at most
![200 m](/media/m/b/d/1/bd180896c21b154ebccdaad32ff674ff.png)
from each vertex of the pentagon. Prove that he stands at a distance of at least
![100 m](/media/m/a/8/a/a8a0ccb5da10c8b67b62ec025e96689e.png)
from each side of the pentagon.
%V0
$(YUG 2)$ 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