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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}.

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