In $Fig.$ a circle is inscribed in a square of side $5 \,cm$ and another circle is circumscribing the square. Is it true to say that area of the outer circle is two times the area of the inner circle? Give reasons for your answer.
In $Fig.$ a circle is inscribed in a square of side $5 \,cm$ and another circle is circumscribing the square. Is it true to say that area of the outer circle is two times the area of the inner circle? Give reasons for your answer.
It is true, because diameter of the inner circle $=5 \,cm$ and that of outer circle $=$ diagonal of the square $=5 \sqrt{2} \,cm$
$So , A _{1}=\pi\left(\frac{5 \sqrt{2}}{2}\right)^{2}$ and $A _{2}=\pi\left(\frac{5}{2}\right)^{2},$ giving $\frac{ A _{1}}{ A _{2}}=2$
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