Math Help

Im trying to program a little Flash game involving a pullstring doll... however Im having a problem involving mathemetics
involving tangents… now you may wonder what pullstring dolls in
Flash have to do with tangents…well… I`ll try to explain…

The Problem:
Im trying to create... a line between a certain point on the doll and a point on the circular "finger handle"... However... I dont know how
to make it so you can contuously set the point on the “circular
handle” on the edge… on the tangent closest to the point on the

In brief:
At the moment the ends of the line are on the center of the doll
(which is desired) and on the center of the “circular finger handle”
(which is not desired)… as I`ve stated… I want the 2nd point of
the line to be on the closest tangent point of the circle. to the
center of the doll…*
So anyway… can anyone help me?