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Complex geo in two consecutive years in Iran

Source: Iranian third round 2019 finals Algebra exam problem 1

August 27, 2019
geometryalgebra

Problem Statement

Let A1,A2,…AkA_1,A_2, \dots A_k be points on the unit circle.Prove that:
∑1≤i<j≤kd(Ai,Aj)2≤k2\sum\limits_{1\le i<j \le k} d(A_i,A_j)^2 \le k^2
Where d(Ai,Aj)d(A_i,A_j) denotes the distance between Ai,AjA_i,A_j.
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