IMO 1985 LL ROM69

Let A and B be two finite disjoint sets of points in the plane

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IMO 1985 LL ROM69

Origin: ROM

Problem

Let A and B be two finite disjoint sets of points in the plane such that any three distinct points in A\cupB are not collinear. Assume that at least one of the sets A, B contains at least five points. Show that there exists a triangle all of whose vertices are contained in A or in B that does not contain in its interior any point from the other set.