ILL 1983 Problem 35

Let $P_1, P_2, \dots , P_n$ be distinct points of the plane, $n \geq 2$. Prove that $$\max_{1\leq i<j\leq n} P_iP_j > \frac{\sqrt 3}{2}(\sqrt n -1) \min_{1\leq i<j\leq n} P_iP_j$$