any circle passing through two points contains at least 673 of others
Source: IGO 2021 Advanced P4
January 2, 2022
geometryIGO
Problem Statement
points on the plane in the convex position, no three collinear and no four concyclic, are given. Prove that there exist two of them such that every circle passing through these two points contains at least of the other points in its interior.
(A finite set of points on the plane are in convex position if the points are the vertices of a convex polygon.)