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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.
Solution
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`
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