MathDB

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

Source:

October 4, 2010

geometrygeometric inequalitypentagoneuclidean distanceIMO ShortlistIMO Longlist

Problem Statement

(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.