A circle `C_1`, of radius `2` touches both `x`-axis and `y`- axis. Another circle `C_2` whose radius is greater than `2` touches circle and both the axes. Then the radius of circle is

Options

A. `3-2sqrt(2)`
B. `3+2sqrt(2)`
C. `3+2sqrt(3)`
D. `6+sqrt(3)`

Answer

2

Explanation

Let the two circles be as shown in the figure.
The smaller circle is `x^(2)+y^(2)=1`.
Clearly, from the figure
`cos 45^(@)=(DE)/(AD)`
`implies (1)/(sqrt(2))=(r-1)/(r+1)`
`implies r+1=sqrt(2)r-sqrt(2)`
`implies r=(sqrt(2)+1)/(sqrt(2)-1)=3+2sqrt(2)`