Question

Three circles are placed on a plane in such a way that each circle
just touches the other two, each having a radius of 10 cm. Find the
area of the shaded region. (Use /3 = 1.732)
​

Answer 1

ANSWER

⇒ Here, AB=BC=AC=10+10=20cm

∴ △ABC is equilateral triangle.

∴ ∠A=∠B=∠C=60

o

⇒ Let a=20cm

⇒ Area of equilateral △ABC=

4

3

×a

2

⇒ Area of equilateral △ABC=

4

3

×(20)

2

∴ Area of equilateral △ABC=

4

400×

3

=173.20cm

2

⇒ Here, θ=60

o

and r=10cm

⇒ Area of 3 sectors =3×

360

o

θ

πr

2

⇒ Area of 3 sectors =3×

360

o

60

o

×

7

22

×(10)

2

∴ Area of 3 sectors =3×52.38=157.14cm

2

⇒ Required area = Area of equilateral triangle - Area of 3 sectors.

⇒ Required area =173.20−157.14=16.06cm

2