7./A chord of a circle of radius 12 cm subtends an
angle of 120° at the centre. Find the area of the
corresponding segment of the circle.
.
(User3.14 and 3 = 1.73)
Answers
Answered by
1
Step-by-step explanation:
REF.Image.
Given→
Radius = 12 cm
∠AOB=120
∘
Area of segement (APB)
= Area of sector APBO
- Area of triangle AOB
=
360
∘
θ
×πμ
2
−
2
1
μ
2
sinθ
=
360
120
×π(12)
2
−
2
1
(12)
2
sin120
∘
=
7×3
144×22
−
2
1
×144×
2
3
=(150.85−62.35)cm
2
=88.40cm
2
Area of △AOB=2×(
2
1
×OD×DB)
=2×
2
1
(rcos
2
θ
)r(sin
2
θ
)
=
2
1
×(2cos
2
θ
sin
2
θ
)r
2
=
2
1
r
2
sinθ
[∵sin2θ=2sinθcosθ]
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