MathDB

70

Part of 1969 IMO Shortlist

Problems(1)

At most 200m implies at least 100 m from each side

Source:

10/4/2010
(YUG2)(YUG 2) A park has the shape of a convex pentagon of area 500003m250000\sqrt{3} m^2. A man standing at an interior point OO of the park notices that he stands at a distance of at most 200m200 m from each vertex of the pentagon. Prove that he stands at a distance of at least 100m100 m from each side of the pentagon.
geometrygeometric inequalitypentagoneuclidean distanceIMO ShortlistIMO Longlist