(i) area of the segment formed by the corresponding chord

Solution:

Provided,

Radius of the circle = 21 cm

θ = 60°

(i)  Area of sector OAPB – Area of ΔOAB = Area of segment APB

OAB is an equilateral triangle since its two arms are the radii of the circle and hence equal, and one angle is 60°.

So, its area will be √3/4×a² sq. Units.

Segment APB area = 231-(√3/4)×(OA)²

= 231-(√3/4)×21²

Alternatively, the APB segment’s area = [231-(441×√3)/4] cm²