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Draw a line parallel to the line joining the centers of the circles from A which will meet the line joining B and the center of the rightmost circle at C . Obviously , the angle ACB will be a right angle , with AC = r₁ + r₂ = 25 and BC = r₂ - r₁ = 7 . Hence , AB = √AC² + BC² = √674

Edit - The small mistake -----Angle ABC is actually 90 degree .

@Ricky

LABC is 90⁰ and not LACB. Which gives AB = 24 units

Thanks a lot for the solution....!