Question 878585
Your explanation is confusing, here's what I've got so far.
You're given two radii: {{{R[A]}}} and {{{R[B]}}}, which can be variables.
Circles A and B cannot overlap. I think that's what you mean by "middle".
I'm guessing you're given the location of circle A's center. 
Then you have to calculate a possible location for circle B's center. 
That's straightforward. You can find a zone to place circle B's center so that it doesn't overlap circle A. 
Now what is the relationship between point C and the centers of the two circles. Does the center of B have to be the maximum distance from point C?
So you're given the coordinates of circle A center({{{x[A]}}},{{{y[A]}}}), circle A radius{{{R[A]}}}, circle B radius{{{R[B]}}}, coordinates of C({{{x[C]}}},{{{y[C]}}}),, and you have to find the maximum distance from the center of circle B to point C within some bounded plane?