A line L separates a set A from a collection S of plane sets if A is contained in one of the closed half-planes defined by L, while every set in S is contained in the complementary closed half-plane. Let f(n) be the largest integer such that for any collection F of n closed disks in the plane with pairwise disjoint interiors, there is a line that separates a disk in F from a subcollection of F with at least f(n) disks. In this note the authors prove that there is a constant c such that f(n)≥(n-c)/2. An analogous result for the d-dimensional Euclidean space is also discussed.
