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Question

A chord of a circle of radius 12 cm subtends an angle of 120 at the centre. Find the area in cm2 of the corresponding segment of the circle. (Use π = 3.14 and 3 = 1.73)


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Solution

The area of the sector = 120360×π×122 = 150.8 cm2

Perpendicular from chord is drawn to the centre bisects the chord. The angle subtended by each triangle at the centre is 60.

Height of perpendicular = r x cos 60 = 12 x 0.5 = 6 cm.

Length of chord = 2 × r × sin 60 = 24 × 32= 20.6 cm

The area of triangle = 0.5 × 20.6 × 6 = 61.8 cm2

The area of segment = 150.8 - 61.8 = 89 cm2


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