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n points lie on 2 circles - All-Russian MO 1998 Regional (R4) 8.4

Source:

September 17, 2024
geometrycombinatoricscombinatorial geometry

Problem Statement

A set of n9n\ge 9 points is given on the plane. For any 9 it points can be selected from all circles so that all these points end up on selected circles. Prove that all n points lie on two circles