How to constrain disks that intersection of them is inside unit circle

Question

I have two disks $(x-a_1)^2+(y-b_1)^2\leq r_1^2$ and $(x-a_2)^2+(y-b_2)^2\leq r_2^2$, where $a_1$, $b_1$, $r_1$, $a_2$, $b_2$, $r_2$ are all known. What kind of constraint can I put on $a_i$, $b_i$ and $r_i$ that the intersection of two disks is inside unit circle? The question is for intersection of two disks, but the generalization for $n$ disks would be even better.