Correct Answer: $7 \mathrm{~cm}$

Solution :
Given,
AD is a diameter
AC is a chord
OB = 7
$\angle{OBA} = 60°$
$\angle{DOC} = 60°$
Now, $\angle{DOC} + \angle{AOC} = 180°$ (The sum of the angles on a straight line is 180°)
⇒ $60° + \angle{AOC} = 180°$
⇒ $ \angle{AOC}= 120° $
In ΔAOC
AO = OC (Radius of the circle)
⇒ $\angle{OAC} = \angle{OCA} = \frac{180° – 120°}{2}$
⇒ $\angle{OAC} = \angle{OCA} = 30° $
⇒ $\angle{OBC} = 180°- 60° = 120°$
⇒ $\angle{ BOC} = (180°- 120° - 30°) = 30°$
⇒ $\angle{ BOC} = \angle{OCB} = 30°$
In ΔBOC,
OB = BC  (Isosceles triangle)
⇒ OB = 7 cm
⇒ BC = 7 cm
Hence, the correct answer is $7 \mathrm{~cm}$.