  G\"unter Ziegler has shown in 1989 that some homological invariants
associated with the free resolutions of Jacobian ideals of line arrangements
are not determined by combinatorics. His classical example involves hexagons
inscribed in conics. Independently, Sergey Yuzvinsky has arrived in 1993 at the
same type of line arrangements in order to show that formality is not
determined by the combinatorics. In this note we look into the geometry of such
line arrangements, and find out an unexpected relation to the classical
Pascal's Theorem. Our results give information on the minimal degree of a
Jacobian syzygy and on the formality of such hexagonal line arrangements in
general, without an explicit choice for the six vertices of the hexagon.
