[math-fun] a circle packing theorem

back in undergraduate complex analysis, i learned the following theorem, whose proof is easy enough using conformal mappings. does this theorem have a name? Let D be a disk entirely inside the unit circle. Consider all collections of non-overlapping disks C so that each member of C is: a) inside the unit circle and tangent to the unit circle, b) doesn't overlap D but is tangent to D, and c) tangent to exactly two other members of C. (Thus the collection C forms a tangent ring around D.) For a given D, the collection is either empty or infinite. erich