Correct option is: (A) 8 cm
We know that radius is perpendicular to tangent at point of contact.
\(\because\) AB is tangent to smaller circle and OP is radius of smaller circle and their point of contact is P.
\(\therefore\) OP \(\perp\) AB
\(\because\) AB is chord of bigger circle and OP \(\perp\) AB.
\(\therefore\) OP bisects AB
(\(\because\) Perpendicular drawn from centre of circle to chord of the circle bisects the chord)
\(\therefore\) AP = PB
Now, in right \(\triangle\) APO,
\(AP^2 = OA^2 - OP^2 = 5^2 - 3^2\) (\(\because\) OA = OB = 5 cm & OP = 3 cm (Given))
= 25 - 9 = 16 = \(4^2\)
\(\therefore\) AP = 4 cm
\(\therefore\) AB = 2 AP = 2 x 4 = 8 cm
