Question

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)​

Answer 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]