MathDB
Distance to lines and points

Source: Kürschák competition 2011 P3

March 2, 2020
combinatorial geometryinequalities

Problem Statement

Given 2n2n points and 3n3n lines on the plane. Prove that there is a point PP on the plane such that the sum of the distances of PP to the 3n3n lines is less than the sum of the distances of PP to the 2n2n points.
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