The ratio of the areas of the greatest and the smallest circles touching $(x \pm 1)^2+(y \pm 1)^2=1$ is

• A

  $\frac{\sqrt{3}+1}{\sqrt{3}-1}$
• B

  $\frac{3+\sqrt{2}}{3-\sqrt{2}}$
• Correct answer
  C

  $\frac{3+2 \sqrt{2}}{3-2 \sqrt{2}}$
• D

  $4$

Solution

(c) Let radius of smaller circle be $r$ and radius of bigger.circle be $R$
$\begin{aligned} r & =\sqrt{2}-1 \\ R & =\sqrt{2}+1 \\ \therefore \text { Ratio of areas } & =\frac{(\sqrt{2}+1)^2}{(\sqrt{2}-1)^2}=\frac{3+2 \sqrt{2}}{3-2 \sqrt{2}}\end{aligned}$

Hence, the correct answer is option: 'C'.