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The centre of variable circle x^2+y^2+ ...

The centre of variable circle `x^2+y^2+ 2gx + 2fy + c = 0` lies on the line `2x-2y +9=0` and the variable circle cuts the circle `x^2+y^2=4` orthogonally. If the variable circle passes through two fixed points (a, b) and (c, d) where (b < d) then the value of 2b + d is equal to

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