Problem #PRU-32032

Problems Algebra and arithmetic Algebraic inequalities and systems of inequalities Linear inequalites and systems of inequalities Methods Pigeonhole principle Pigeonhole principle (angles and lengths) Geometry Plane geometry Geometrical inequalities Triangle inequality Triangle inequality (other)
 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.