Question 878593
{{{drawing(400,400,-11,11,-5,17,green(circle(-2,8,2*sqrt(2))),circle(-2,8,0.2),line(-2,8,5,15),blue(circle(0,10,2)),circle(0,10,0.2),circle(5,15,0.2),locate(0.5,10.5,B),locate(-3,8,A),locate(5.9,15,C))}}}

OK, I think I get it now.
The blue circle is circle B.
The green circle is circle A.
The dot is C. 
The green circle is located at the maximum distance from C while still capturing the center of circle B along its circumference. 
Once you know the location of C and circle B, you know the direction of the center of circle A because the three points are collinear. 
The maximum distance is then the distance from C to center of B plus the radius of B plus the radius of A.
You can email me to verify that this is the correct setup and then we can work on a solution.