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$C_{1}$ is a circle of radius 1 touching the x-axis and y-axis. $C_{2}$ is another circle of radius greater than 1 and touching the axes as well as the circle $C_{1}$ . Then, the radius of $C_{2}$ is

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$3 - 2 \sqrt{2}$

$3 + 2 \sqrt{3}$

$3 + 2 \sqrt{2}$

answer is B.

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Detailed Solution

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Or $25 - n^{2} > 4$
From the diagram, sin $45^{o} = \frac{A B}{O A} = \frac{r}{O C + C D + D A}$
$= \frac{r}{\sqrt{2} + 1 + r}$
Or $\sqrt{2} + 1 + r = \sqrt{2} r$
Or $r = \frac{\sqrt{2} + 1}{\sqrt{2} - 1} = 3 + 2 \sqrt{2}$

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