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. | 