  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 $x,y \in P$ the line
through $x$ and $y$ contains a point in $R$ outside of the segment delimited by
$x$ and $y$. We show that $P \cup R$ must be contained in a cubic curve.
