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Question

A chord of a circle of radius 12 cm subtends an angle of 120 at the center. Find the area of the corresponding segment of the circle.

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Solution

REF.Image.
Given
Radius = 12 cm
AOB=120
Area of segement (APB)
= Area of sector APBO
- Area of triangle AOB
=θ360×πμ212μ2sinθ
=120360×π(12)212(12)2sin120
=144×227×312×144×32
=(150.8562.35)cm2
=88.40cm2
Area of AOB=2×(12×OD×DB)
=2×12(rcosθ2)r(sinθ2)
=12×(2cosθ2sinθ2)r2
=12r2sinθ
[sin2θ=2sinθcosθ]

1114581_1201736_ans_d800638ac895440c9f36178bf8d21de1.jpg

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