XY is a chord of circle centre O and radius 7cm. The chord XY which is 8cm long subtends an angle of 120o at the centre of the circle. Calculate the perimeter of the minor segment. [Take \(\pi = \frac{22}{7}\)]
A
14.67cm
B
22.67cm
C
29.33cm
D
37.33cm
Verified Correct Answer: B.
Step-by-Step Mathematical Solution
perimeter of minor segment = Length of arc xy + chord xy
where lxy = \(\frac{120}{360} \times 2x \times \frac{22}{7} \times 7\)
= 14.67cm
perimeter of minor segment = 14.67 + 8 = 22.67cm
Source: Myschool Past Questions Archive (Record #36386)