Question

$C_1$ is circle of radius $1$ touching the x-axis and the $y$-axis. $C_2$ is also circle of radius $>1$ 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

Answer: (B)

$3+2\sqrt{2}$

equation of circle $C_1$ is $(x-1{)}^2+(y-1{)}^2=1$
let the center of $C_2$ be $(h,h)$ and its radius is $h$
Since, they touch each other
Therefore, $C_1{C}_2=r_1+r_2$
$\Rightarrow \sqrt{{(h-1)}^2+{(h-1)}^2}=h+1$
Solving for h, we get $h=3+2\sqrt{2}$
Ans: B