Calculate rectangle inside ring parameters

Question

Imagine we have a rectangle (with sides A, B) that fits into the ring (r1, R2).

If r1, A and B are known, what is the equation for R2? (that is in my particular case)

What are the interrelations between r1, R2, A, B?

Answer 1

Ok... Basically it goes to Circular Segment calculation (Circular Segment on wolfram)

In terms of this picture:

$4r^2 = 4R^2 - a^2$

In terms of my original picture and question where $r = r_{1} + B$

$4(r_{1} + B)^{2} = 4R_{2}^{2} - A^2 $

and

$R=\sqrt{(r_{1}+B)^{2} + \frac{A^{2}}{4}}$