A finite set of unit circles is given in a plane such that the area of their union
![U](/media/m/d/f/a/dfa3ccb1bb2d14869d77a98d0d2baf97.png)
is
![S](/media/m/c/6/3/c63593c3ec0773fa38c2659e08119a75.png)
. Prove that there exists a subset of mutually disjoint circles such that the area of their union is greater that
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A finite set of unit circles is given in a plane such that the area of their union $U$ is $S$. Prove that there exists a subset of mutually disjoint circles such that the area of their union is greater that $\frac{2S}{9}.$