Your description of the problem leaves a lot of freedom in how to set it up. Here is one of many ways to do it.

Let the first circle with the yellow box be the set of points

Let the second circle with the green box be the set of points

where M is a rotation matrix (orthogonal, determinant = 1).

Let L be the length of the line connecting the boxes and let x be the coordinates of the yellow box and x' be the coordinates of the the green box. Then for a given the solution(s) x to

"describes" the yellow box x in terms of the green box x'.