MathDB
Finite set of unit circles

Source:

September 15, 2010
geometrycirclesareaIMO Shortlist

Problem Statement

A finite set of unit circles is given in a plane such that the area of their union UU is SS. Prove that there exists a subset of mutually disjoint circles such that the area of their union is greater that 2S9.\frac{2S}{9}.
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