IMO ShortList 1999, geometry problem 2
Source: IMO ShortList 1999, geometry problem 2
November 13, 2004
geometrypoint setcirclescombinatorial geometryIMO Shortlist
Problem Statement
A circle is called a separator for a set of five points in a plane if it passes through three of these points, it contains a fourth point inside and the fifth point is outside the circle. Prove that every set of five points such that no three are collinear and no four are concyclic has exactly four separators.