Question

O and O' are the centre's of two congruent circles of radius 8 cm . What is the area of the shaded region in cm2?

Answer 1

Answer:

Since circumference of circle = 2πr

⇒2=2πr

⇒r=1/πcm for both circles

From symmetry, perpendicular AB to

O  

1

​  

O  

2

​  

 also bisects O  

1

​  

O  

2

​  

 

As O  

1

​  

O  

2

​  

=r=  

π

1

​  

cm

(O  

1

​  

 is center for O  

1

​  

 and O  

2

​  

 lies on its circumference)

⇒O  

1

​  

L=  

2

1

​  

×  

π

1

​  

=  

2π

1

​  

cm

and O  

1

​  

A=r=  

π

1

​  

cm

⇒ In △O  

1

​  

AL, cosθ=  

O  

1

​  

A

O  

1

​  

L

​  

=  

2π

1

​  

×π=  

2

1

​  

 

⇒θ=60  

∘

=  

3

π

​  

 

As we know angle =  

radius

arc

​  

 

for arc AB of circle C  

1

​  

,

arc=2θ×r=2×  

3

π

​  

×  

π

1

​  

=  

3

2

​  

cm

Similarly arc AB of circle C  

2

​  

=  

3

2

​  

cm

Perimeter of shaded region = AO  

1

​  

B+AO  

2

​  

B=  

3

4

​  

cm

solution

Step-by-step explanation: