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AD,CD \cap [ABC] is empty

Source: Saint Petersburg olympiad 2024, 11.5

September 22, 2024
geometrycombinatorial geometry

Problem Statement

There are 100100 points of general position marked on the plane (i.e. no three lie on the same straight line). Prove that it is possible to select three marked points A,B,CA, B, C so that for any point DD of the remaining 9797 marked points, the lines ADAD and CDCD would not contain points lying inside the triangle ABCABC.
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