On sets of n points in general position that determine lines that can be pierced by n points
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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.
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