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Question

Find the ratio of the areas of the incircle and circumcircle of a square.


A

1:1

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B

1:2

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C

1:3

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D

1:4

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Solution

The correct option is B

1:2


Let the side of the square be x.

Then, its diagonal = 2x

Radius of incircle = x2

AO is the radius of cicum circle but it is also hypotnuse of an isoscles triangle with side x2.

So,radius of circum circle= 2 x x2 = x2

Required ratio = πx24 : πx22 = 14 : 12 = 1 : 2


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