IMO Shortlist 1983 problem 17
Dodao/la:
arhiva2. travnja 2012. Let
![P_1, P_2, \dots , P_n](/media/m/b/f/6/bf6ad0cf14e8bdc2f06abef845a45719.png)
be distinct points of the plane,
![n \geq 2](/media/m/b/f/d/bfd49780fcd06b84db1ffa706541d364.png)
. Prove that
%V0
Let $P_1, P_2, \dots , P_n$ be distinct points of the plane, $n \geq 2$. Prove that $$\max_{1 \leq i<j \leq n} P_iP_j > \frac{\sqrt 3}{2}(n -1) \min_{1 \leq i<j \leq n} P_iP_j$$
Izvor: Međunarodna matematička olimpijada, shortlist 1983