Problem

Source: Iranian third round 2019 finals Algebra exam problem 1

Tags: geometry, algebra



Let $A_1,A_2, \dots A_k$ be points on the unit circle.Prove that: $\sum\limits_{1\le i<j \le k} d(A_i,A_j)^2 \le k^2 $ Where $d(A_i,A_j)$ denotes the distance between $A_i,A_j$.