Can someone help ms in this limit problem

Let E be a bounded, closed set of infinitely many points in the plane. Define the separation of a (possibly concave) polygon as the geometric mean of the lengths of all of its diagonals and edges. For each integer n > 2 let s_{n} be the maximum possible separation of an n-gon with vertices in E.

Prove that lim n -> ∞ s_{n} exists.