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Lots of points

Source: RMO 2006

April 18, 2006
inequalitieslimitcomplex numbersreal analysisreal analysis unsolved

Problem Statement

We have in the plane the system of points A1,A2,…,AnA_1,A_2,\ldots,A_n and B1,B2,…,BnB_1,B_2,\ldots,B_n, which have different centers of mass. Prove that there is a point PP such that PA1+PA2+…+PAn=PB1+PB2+…+PBn. PA_1 + PA_2 + \ldots+ PA_n = PB_1 + PB_2 + \ldots + PB_n .
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