Apollonius Revisited Equidistance

Distance between: Two external circles P, Q is AB, which is created by joining thecenters P&Q and removing the two radii, R & r.Thus AB= PQ-(PA+QB). AB=PQ-(R+r)= PQ " R " r!Distance between: Two circles, Q inside P, is AB, which is created by joining the centersP&Q with a ray and removing the distance between the centers and the smaller radius. r,from the bigger radius, R. Thus AB=PA-(PQ+QB)=R-(PQ+r)= PQ " R " r!Exercise: If two circles are tangent or intersecting the distance between them should bezero. Do the definitions given allow for this situation? How do the distance formulasdetect these cases?