Question
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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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Answer: Option A
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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 = 150.8Â - 61.8 = 89Â cm2
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