Question

$C_1$ is a circle of radius $1$ touching the x-axis and the y-axis. $C_2$ is another circle of radius $>1$ and touching the axes as well as the circle $C_1$. Then, the radius of $C_2$ is

• A. $3-2\sqrt{2}$
• B. $3+2\sqrt{2}$
• C. $3+2\sqrt{3}$
• D. None of these

Answer 1

The correct option is B $3+2\sqrt{2}$

$25-n^2>4$
From the diagram $\sin {45}^o=\frac{AB}{OA}$
$=\frac{r}{OC+CD+DA}$
$=\frac{r}{\sqrt{2}+1+r}$
$\Rightarrow \sqrt{2}+1+r=\sqrt{2}r$
$\Rightarrow r=\frac{\sqrt{2}+1}{\sqrt{2}-1}=3+2\sqrt{2}$