A chord PQ of length 12 cm subtends an angle of 120° at the centre of a circle. Find the area of the minor segment cut off by the chord PQ.

Question

A chord PQ of length 12 cm subtends an angle of 120&#xB0; at the centre of a circle. Find the area of the minor segment cut off by the chord PQ.

Philoid · Accepted Answer

Length of chord PQ = 12cm

Angle subtend at the center = 120°

Let radius of circle = r cm

Area of sector =

Length of triangle POQ = r cos 60

Length of base PQ = 2×RQ

Put value of r in respective place,

Area of minor segment = area of sector – area of ∆POQ