Question

A chord of a circle of radius 14 cm makes a right angle at the centre. Find the areas of the minor and major segments of the circle. 

Answer 1

Given,

Radius (r) = 14 cm

Angle subtended by the chord with the centre of the circle, θ = 90°

Area of minor segment = θ/360 x πr² – 1/2 x r² sin θ

= 90/360 x π(14)² – 1/2 x 14² sin (90)

= 1/4 x (22/7) (14)² – 7 x 14

= 56 cm²

Area of circle = πr²

= 22/7 x (14)² = 616 cm²

Thus,

The area of the major segment = Area of circle – Area of the minor segment

= 616 – 56

= 560 cm²