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points contained in two different circles

Source: 2021 Iran second round mathematical Olympiad P4

May 16, 2021
geometrycombinatoricscombinatorial geometry

Problem Statement

nn points are given on a circle ω\omega. There is a circle with radius smaller than ω\omega such that all these points lie inside or on the boundary of this circle. Prove that we can draw a diameter of ω\omega with endpoints not belonging to the given points such that all the nn given points remain in one side of the diameter.
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