Let
![n\geq3](/media/m/e/1/a/e1ac2e5ac682ff0ae2f50c498d8168b2.png)
be a positive integer. Let
![C_1,C_2,C_3,\ldots,C_n](/media/m/8/a/6/8a622a02e402bcf5e195dc2d7f591ae0.png)
be unit circles in the plane, with centres
![O_1,O_2,O_3,\ldots,O_n](/media/m/c/1/6/c1632d0e809b1027f0f9911924b8f69e.png)
respectively. If no line meets more than two of the circles, prove that
%V0
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 $$\sum\limits^{}_{1\leq i<j\leq n}{1\over O_iO_j}\leq{(n-1)\pi\over 4}.$$