Question

In the following figure, ABCD is a square of side 2a, Find the ratio between

(i) the circumferences

(ii) the areas of the in circle and the circum-circle of the square. 

Answer 1

We have a square ABCD having`AB=2c`. From the given diagram we can observe that,

Radius of incircle `(r_1)=a`

Radius of circumcircle `(r_2)=sqrt2a`

(i) We have to find the ratio of the circumferences of the two circles. So the required ratio is,

=` "Perimeter of inner circle "/"Perimeter of circumcircle" ` 

`=(2pi(a))/(2 pi(sqrt2a))`

`= 1/sqrt2`

(ii) We have to find the ratio of the areas of the two circles. So the required ratio is,

`= "Area of inner circle"/"Area of circumcircle"`

`= (pi(a)^2)/(pi(sqrt2a)^2)`

`=1/2`