The best strategy will indeed be of calculating your way through this. Since you have three circles that represent your mass, you have their centers and radii, I assume.
1- Calculate the center of mass (xc, yc) of the whole system. There must be a way to do in Vision. Else, use a ponderated way using the radius of each circle. (A smaller circle would move the center of mass less than a larger circle...)
2- Find the extrema for each directions: i.e. for each circles, calculate the point furthest in each direction. (You need only the four cardinal directions if you're dealing with circles.)
For example:
center of circle1 = (x1, y1) and radius = r1
then left bound = (x1-r1, y1), low bound = (x1, y1-r1), etc.
Calculate for each circles and keep the maximum in each directions.
3-Your minimum radius circle that encompasses all circles will be of the same radius as the maximum distance between the center of mass and any of those bounds.
4- Draw your circle from (xc, yc) with a radius rc = distance between (xc, yc) & largest (xn±rn, yn±rn).
I hope this doesn't sound too complicated...