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Two circles C1a n dC2 both pass through ...

Two circles `C_1a n dC_2` both pass through the points `A(1,2)a n dE(2,1)` and touch the line `4x-2y=9` at `Ba n dD ,` respectively. The possible coordinates of a point `C ,` such that the quadrilateral `A B C D` is a parallelogram, are `(a ,b)dot` Then the value of `|a b|` is_________

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