The dual colorful Tverberg theorem in the plane

Let $3n$ straight lines in general position be given in the plane, and partition them into three color classes of $n$ lines each. The dual colorful Tverberg theorem. The lines can be partitioned into $n$ colorful triples, each containing one line of every color, such that the triangles formed by the triples have a common point. This is proposed as a dual analogue of the colorful Tverberg theorem in the plane; the supplied text does not state whether it has been proved or remains open.