Dirac and Motzkin conjectured that any set \(\mathcal {X}\) of n non-collinear points in the plane has an element incident with at least \(\lceil \frac{n}{2} \rceil \) lines spanned by \(\mathcal {X}\) . In this paper we prove that any set \(\mathcal {X}\) of n non-collinear points in the plane, distributed on three lines passing through a common point, has an element incident with at least \(\lceil \frac{n}{2} \rceil \) lines spanned by \(\mathcal {X}\) .
