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Angles covering the plane

Source: Brazilian Olympic Revenge 2020, P5

February 1, 2020
combinatoricscombinatorial geometryolympic revengeBrazil

Problem Statement

Let nn be a positive integer. Given nn points in the plane, prove that it is possible to draw an angle with measure 2πn\frac{2\pi}{n} with vertex as each one of the given points, such that any point in the plane is covered by at least one of the angles.
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