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Problem 9 IMC 2004 Macedonia

Source:

July 26, 2004
inequalitiestriangle inequalityIMCcollege contests

Problem Statement

Let DD be the closed unit disk in the plane, and let z1,z2,…,znz_1,z_2,\ldots,z_n be fixed points in DD. Prove that there exists a point zz in DD such that the sum of the distances from zz to each of the nn points is greater or equal than nn.
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