On Sets of n Points in General Position That Determine Lines That Can Be Pierced by n Points

Abstract

Let P be a set of n points in general position in the plane. Let R be a set of n points disjoint from P such that for every x, y ∈ P the line through x and y contains a point in R outside of the segment delimited by x and y. We show that P ∪ R must be contained in a cubic curve.