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.
i.e. yc=(ma*ya+mb*yb)/(ma+mb);
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.

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