Given a set $\mathcal{R}$ of m disjoint finite regions in the 2-dimensional plane, all regions having polygonal boundaries, and given a set $\mathcal{D}$ of n discs with fixed centers and radii, we consider the problem of finding a minimum cardinality subset $\mathcal{D}^*\subseteq \mathcal{D}$ such that every point in $\mathcal{R}$ is covered by at least one disc in $\mathcal{D}^*$. We show that this problem can be solved by using an iterative procedure that alternates between the solution of a traditional set-cover problem and the construction of the Laguerre-Voronoi diagram of a circle set.