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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`A. `a=13`B. `b=3`C. `c=2`D. `a=17` |
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Answer» Correct Answer - B::C::D 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)` |
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