KöMaL 2006 A397

Given $n$ unit circle ($n \ge$3) in the plane, their centers are $O_1$,$O_2$,...,$O_n$. Any line of the plane intersects at most two of them. Show that $\sum_{1\le i<j\le n}\frac1{O_iO_j}\le\frac{(n-1)\pi}4.$