perimeter of triangle with vertices within three specified circles

Given three circles with radii r1,r2, and r3 whose centers are distances a,b, and c away from each other, find a triangle with the maximum perimeter where each vertex of the triangle intersects a different circle. For example, for a=b=c=3 and r1=r2=r3=1, the answer is 14.196. For given values of r1,r2,r3,a,b, and c I can solve it numerically, but I am stuck trying to come up with a purely symbolic solution.

Any help would be appreciated.