Let $n$ unit circles be given on a plane. Prove that on one of the circles there is an arc of length at least $\frac{2\pi}n$ not intersecting any other circle.
Source: Bulgaria 1982 P2
Tags: circles, geometry
Let $n$ unit circles be given on a plane. Prove that on one of the circles there is an arc of length at least $\frac{2\pi}n$ not intersecting any other circle.