Question

A circle is inscribed in an equilateral triangle of sides 18 cm. Find the area between
the triangle and the circle. (take 13 =1.73).
​

Answer 1

Answer:

Step-by-step explanation:

Here, AB=BC=AC=12cm

⇒ Let OP=OR=OQ=r

⇒ We have O as the incenter and OP,OQ and OR are equal.

⇒ ar(△ABC)=ar(△OAB)+ar(△OBC)+ar(△OCA)

4

3

​

​

×(side)

2

=(

2

1

​

×OP×AB)+(

2

1

​

×OQ×BC)+(

2

1

​

×OR×AC)

⇒

4

3

​

​

×(12)

2

=(

2

1

​

×r×12)+(

2

1

​

×r×12)+(

2

1

​

×r×12)

⇒

4

3

​

​

×(12)

2

=3(

2

1

​

×12×r)

∴ r=

18

36

3

​

​

∴ r=2

3

​

cm

⇒ Area of the shaded region = Area of △ABC - Area of circle.

⇒ Area of the shaded region =

4

3

​

​

×(12)

2

−

7

22

​

×(2

3

​

)

2

⇒ Area of the shaded region =(62.35−37.71)cm

2

=24.64cm

2