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# If area of the given circle is $$\Large 100 \pi$$ square cm, then side of the square inscribed in the circle is

 A) 10 cm B) $$\Large 10\sqrt{2}\ cm$$ C) 20 cm D) $$\Large 20\sqrt{2}\ cm$$

 B) $$\Large 10\sqrt{2}\ cm$$

If r is the radius of the circle, then

area of the circle = $$\Large \pi r^{2} = 100 \pi cm^{2}$$

=> $$\Large r^{2} = 100$$ ...(i)

=> $$\Large r = 10 cm$$

From the given figure,

$$\Large x^{2}+x^{2}=r^{2}$$

=> $$\Large 2x^{2}=r^{2}$$ ...(ii)

side of the square = 2x

=$$\Large 2\sqrt{\frac{r^{2}}{2}}=\sqrt{2}r=10\sqrt{2} cm$$

Part of solved Loci and concurrency questions and answers : >> Elementary Mathematics >> Loci and concurrency

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