If the circle `C_(1)` touches x-axis and the line `y=xtantheta(tanthetagt0)` in first quadrant and circle`C_(2)` touches the `y=xtantheta` at the same point at which `C_(1)` touches it such that ratio of radius of `C_(1)` and `C_(2)` is 2:1, then `tan(theta)/(2)=sqrt(a-B)/(c)` where a,b,c,epsilon N and `HCF(b,c)=1`

Options

A. `a=13`
B. `b=3`
C. `c=2`
D. `a=17`

Answer

B, C, D

Explanation

Let `m=tantheta` ,then
`angleAOO_(1)=(theta)/(2),angleO_(2)OO_(1)=45^(@)`
`impliesangleAOO_(2)=45^(@)-(theta)/(2)`
`tan,(theta)/(2)=(r_(1))/(OA)`
`tan (45^(@)-(theta)/(2))=(r^(2))/(OA)`
`(1)/(tan.(theta)/(2))((1-tan.(theta)/(2)))/((1+tan.(theta)/(2)))=(r_(2))/(r_(1))=(1)/(2)`
`impliestan(theta)/(2)=(-3+sqrt(17))/(2)`