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

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.

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unit circle centered at any particular point? – Sasha Sep 2 '12 at 3:51
I guess it doesn't matter, but, maybe you want $r_1^2$ and $r_2^2$ for the sake of geometric clarity. – James S. Cook Sep 2 '12 at 3:51
@Sasha, i have to define $a_i$, $b_i$ and $r_i$, so i think they can be centered any point – kotoll Sep 2 '12 at 3:54
@JamesS.Cook equations are edited. – kotoll Sep 2 '12 at 3:55
I am still looking for suggestions? – kotoll Sep 21 '12 at 23:25