IMO Shortlist 1999 problem G2

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Dodao/la: arhiva
2. travnja 2012.
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.
Izvor: Međunarodna matematička olimpijada, shortlist 1999