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Existence of disk in square not intersecting polygons.

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September 29, 2010
geometryperimeterrectangleconvex polygonIMO LonglistIMO Shortlist

Problem Statement

(BUL3)(BUL 3) One hundred convex polygons are placed on a square with edge of length 38cm.38 cm. The area of each of the polygons is smaller than πcm2,\pi cm^2, and the perimeter of each of the polygons is smaller than 2πcm.2\pi cm. Prove that there exists a disk with radius 11 in the square that does not intersect any of the polygons.
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