Question

Consider following diagram $:AC$ is a diameter of the large circle and $AB=BC$.
The ratio of area of the large circle to the small circle of a square is

• A. $4:1$
• B. $1:4$
• C. $2:1$
• D. $1:2$

Answer 1

The correct option is C $2:1$

$\begin{array}{c}{a}^2+a^2={\left(2x\right)}^2\\ \Rightarrow 4x^2=2a^2\\ \Rightarrow \left(a-\sqrt{2x}\right)\\ Radiofsmallcircle=\frac{\sqrt{2}x}{2}=\frac{x}{\sqrt{2}}\\ Now,\\ \frac{Areaoflecircle}{Areaofsmallcircle}=\frac{\pi x^2}{\pi {\left(\frac{x}{\sqrt{2}}\right)}^2}=2:1\\ Hence,theoptionCisthecorrectanswer.\end{array}$