Do you mean that A and B are both doing circular motion around the center of the system (center of mass of A and B)?
The position of A and B can be random.
If the position of A and B are xa and xb, then the center of mass of the system is xc=(ma*xa+mb*xb)/(ma+mb);
You can get similar equation for ya and yb.
For the particle to be in circular motion, the velocity need to be perpendicular to the radial direction.
And ma*va+mb*vb=0; to prevent drift motion
the centripetal force f=m*v^2/r
You have all the equations you need now.
You are welcomed to check out http://www.phy.ntnu.edu.tw/ntnujava/index.php?topic=2184.0