We say that a set of closed circular discs of radii r1r2, …, all lying in a Euclidean plane, is saturated if and only if r = inf ri > 0 and any circle of radius r has at least one point in common with a circle of the set. For any set X we use α(X) to denote the area of X. If X denotes the point set union of the discs and X(k) the part of X inside the disc whose centre is the origin and radius k then by the lower density of the covering we mean . The problem is to find the exact lower bound of the lower density for any saturated set of circles. We show that it is φ/(6√3) provided the circles are disjoint. The general case, when they may overlap, remains unsolved.