Question 17
(GDR 3) Let $P_1,P_2,\ldots,P_n$ be distinct points of the plane, $n\ge2$. Prove that
$$\max_{1\le i\lt j\le n}P_iP_j>\frac{\sqrt3}{2}(\sqrt n-1)\min_{1\le i\lt j\le n}P_iP_j.$$
$$\max_{1\le i\lt j\le n}P_iP_j>\frac{\sqrt3}{2}(\sqrt n-1)\min_{1\le i\lt j\le n}P_iP_j.$$