Given a set of n disks in the plane, we study the problem of finding k lines that together intersect the maximum number of input disks. We consider three variants of this problem with the following constraints on the solution: (1) no constraint on the lines, (2) the k lines should be parallel and (3) the k lines should pass through a common point. For k = 2 , we give O (n 3 log n) -time algorithms for all three cases. For any fixed k ≥ 3 , we give an O (n 3 k / 2) -time algorithm for (1). For variants (2) and (3), the running times of our algorithms vary from O (n 4) to O (n 6) . [ABSTRACT FROM AUTHOR]