calculating the effect of inaccurate triangle vertex positions on the edge lenghts

i'm not sure how to solve the following problem:

i have a triangle with each of the three known vertex positions A,B,C being inaccurate, meaning they can each deviate up to certain known radii rA, rB, rC into arbitrary directions.

given such a triangle, i want to find out how much the difference of two specific edge lengths a and b of the triangle may change. is this somehow possible without for instance calculating all 360^3 angle combinations and measuring the edge differences for each case?

any help or pointers would be greatly appreciated!