question_answer

Find the ratio of area of encircle and circumcircle of a square:

A)  \[1:2\]                          

B)  \[\sqrt{2}:1\]

C)  \[2:3\]                          

D)  \[\sqrt{3}:1\]

Correct Answer: A

Solution :

     Let the side of square = a Incircle radius of square \[=\frac{a}{2}\] Circumcircle radius of square \[=\frac{Diagonal}{2}=\frac{a\sqrt{2}}{2}\] Ratio of Area \[=\frac{Incircle\,area}{Circumcircle\,area}\] \[=\,\frac{\pi \frac{{{a}^{2}}}{4}}{\frac{\pi \times 2{{a}^{2}}}{4}}=\underline{\mathbf{1:2}}\]