  We give exact and approximation algorithms for two-center problems when the
input is a set $\mathcal{D}$ of disks in the plane. We first study the problem
of finding two smallest congruent disks such that each disk in $\mathcal{D}$
intersects one of these two disks. Then we study the problem of covering the
set $\mathcal{D}$ by two smallest congruent disks.
