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Let S1 and S2 be two variable circles wh...

Let `S_1 and S_2` be two variable circles whose centres lie in different members of family of circles `x^2+y^2 -2x cos theta-2y sintheta-3=0` and pass through a fixed point `(9,sqrt(243))`. The maximum difference of the radii of `S_1 and S_2` is

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