Q17 Matemática  (IMO Shortlist 1983)

Sejam $P_1,P_2,\dots ,P_n$ pontos distintos do plano, $n\ge 2$. Prove que $$\underset{1\le i<j\le n}{\max }{P}_i{P}_j>\frac{\sqrt{3}}{2}(\sqrt{n}-1)\underset{1\le i<j\le n}{\min }{P}_i{P}_j$$