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Problem #PRU-32032

Problemas Álgebra Desigualdades algebraicas y sistemas de desigualdades Desigualdades lineales y sistemas de desigualdades Métodos Principio del casillero Principio del casillero (ángulos y longitudes) Geometría Geometría plana Desigualdades geométricas Desigualdad del triángulo Desigualdad del triángulo (otros)
 13–14  3.0

Problem

On a plane, there are 1983 points and a circle of unit radius. Prove that there is a point on the circle, from which the sum of the distances to these points is no less than 1983.

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