  In the present note we focus on conic line arrangements in the plane with
quasihomogeneous ordinary singularities from the perspective of weak Ziegler
pairs. The foundations of this article come from an active area of research
devoted to the freeness and nearly freeness of curve arrangements in the
complex projective plane and the socalled Numerical Terao s Conjecture. This
conjecture boils down to a very fundamental problem in combinatorial algebraic
geometry, namely whether the weak combinatorics of a given arrangement
determines the freeness.
