question_answer

The ratio of the areas of the in circle and circumcircle of a square are

A) 1 : 1     

B)  2 : 1    

C)  1 : 2    

D)  3 : 1

Correct Answer: C

Solution :

Let side \[AB=BC=CD=AD=x\] Diagonal \[=\sqrt{2}x\] \[\therefore \]      Radius of incircle \[=\frac{x}{2}\] Radius of circumcircle \[=\frac{\sqrt{2}x}{2}=\frac{x}{\sqrt{2}}\] \[\therefore \] Required ratio\[=\left( \frac{\pi {{x}^{2}}}{4}:\frac{\pi {{x}^{2}}}{2} \right)=2:4=1:2\]