Let be a positive integer. Let be unit circles in the plane, with centres respectively. If no line meets more than two of the circles, prove that
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Let $n\geq3$ be a positive integer. Let $C_1,C_2,C_3,\ldots,C_n$ be unit circles in the plane, with centres $O_1,O_2,O_3,\ldots,O_n$ respectively. If no line meets more than two of the circles, prove that $$\sum\limits^{}_{1\leq i<j\leq n}{1\over O_iO_j}\leq{(n-1)\pi\over 4}.$$
Izvor: Međunarodna matematička olimpijada, shortlist 2002
Školjka 
be a positive integer. Let 
be unit circles in the plane, with centres 
respectively. If no line meets more than two of the circles, prove that 