AB is tangent to the inner circle, consider the trigonometric circle.
Knowing the radius of both circles, is there a relation between those 2 point's coordinates ?
Their coordinate being $A = (R \cos(\alpha)$, $R \sin(\alpha))$ and $B = (R \cos(\beta)$, $R \sin(\beta))$, $\alpha$ and $\beta$ being the angle formed by the arcs $A$ and $B$.
Meaning that for example if I know $A$, could I calculate $B$, or vice versa ?