Let "A" be the large disk, and let "B" and "C" be the two smaller disks.

Disk A can't be covered unless its circumference, which is circle A, is covered by the smaller disks.

If disk B covers any of circle A, then it covers a single contiguous arc, because two circles can intersect in at most two points.

Disk B can't cover a diameter of disk A, so the arc of A covered by disk B subtends a central angle of less than 180º.

Similarly, the arc of A covered by disk C subtends a central angle of less than 180º, so together, disks B and C leave part of the circumference of disk A uncovered.