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Question

If a square is inscribed in a circle, then the ratio of the areas of the circle and the square is 


A
π:2
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B
2:π
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C
πr:2
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D
2:πr
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Solution

The correct option is A $$ \pi : 2 $$
Let side of square = a 
radius of circle = r
From $$\triangle OEB$$
$$\triangle OEB$$ is right angled triangle
Applying pythagoroes theorem
$$OE^2 +EB^2=OB^2$$
$$\displaystyle \left(\frac{a}{2}\right)^2+\left(\frac{a}{2}\right)^2=r^2$$
$$\displaystyle 2 \frac {a^2}{4}r$$
$$a^2=2r^2$$
$$a=\sqrt{2}r^2$$
$$\displaystyle \frac {Area \,of \,circle}{Area\, of \,square}=\frac{\pi r^2}{a^2}=\frac{\pi r^2}{2r^2}= \pi : 2$$
1169001_330929_ans_dd42a521f12e4041ab2b30ec35ce7f1c.png

Mathematics

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