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
B
2:π
C
πr:2
D
2:πr

Solution

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

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