Take the intersection of line AB and CD as point E.

EB = ED as tangents from a single point to a circle are equal

EB = EC + CD take EC = x

=> EB = x+ 24

Also AE=EC = x using same explanation above.

AB = AE+EB = x+x+24 = 2x+24 = even number- if you are short of time you can easily guess.

Now triangle ECO is similar to triangle triangle EDO' where O and O' are center of 1st and 2nd respectively.

=>\(\frac{EC}{OD} = \frac{O'D}{ED}\)

=> \(\frac{x}{5}= \frac{5}{(x+24)}\)

=> \(x^2 +24x -25 = 0\)

=> \((x +25)*(x-1)= 0\) => \(x =1\)

=> AB\(= 2x*+24 = 2+24 = 26\)

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