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Every triangle whose three vertices are elements of S

Source: IMO ShortList 1991, Problem 8 (NET 1)

August 15, 2008

combinatoricspoint setTrianglecombinatorial geometryIMO Shortlist

Problem Statement

S

be a set of

n

points in the plane. No three points of

S

are collinear. Prove that there exists a set

P

containing 2n \minus{} 5 points satisfying the following condition: In the interior of every triangle whose three vertices are elements of

S

lies a point that is an element of

P.