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points on the same circle

Source: Baltic Way 2021, Problem 9

November 15, 2021
combinatoricscombinatorics proposed

Problem Statement

We are given 20212021 points on a plane, no three of which are collinear. Among any 55 of these points, at least 44 lie on the same circle. Is it necessarily true that at least 20202020 of the points lie on the same circle?
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