MathDB

19

Part of 1981 IMO Shortlist

Problems(1)

Finite set of unit circles

Source:

9/15/2010
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}.
geometrycirclesareaIMO Shortlist