Školjka

%V0 Let $P_1, P_2, \dots , P_n$ be distinct points of the plane, $n \geq 2$. Prove that $$\max_{1 \leq i<j \leq n} P_iP_j > \frac{\sqrt 3}{2}(n -1) \min_{1 \leq i<j \leq n} P_iP_j$$