The range of values of `lambda,(lambda>0)` such that the angle `theta` between the pair of tangents drawn from `(lambda,0)` to the circle `x^2+y^2=4` lies in `(pi/2,(2pi)/3)` is (a) `(4/(sqrt(3)),2/(sqrt(2)))` (b) `(0,sqrt(2))` (c) `(1,2)` (d) none of these

Options

A. `(4//sqrt(3),2sqrt(2))`
B. `(0,sqrt(2))`
C. `(1,2)`
D. none of these

Answer

1

Explanation

We have `(pi)/(2) lt theta lt (2pi)/(3), `i.e., `(pi)/(4) lt (theta)/(2) lt (pi)/(3)`
or `(1)/(sqrt(2))lt sin . (theta)/(2) lt (sqrt(3))/(2)`
But `sin. (theta)/(2)=(2)/(lambda)` or `(1)/(sqrt(2)) lt (2)/(lambda) lt (sqrt(3))/(2)`
or `(4)/(sqrt(3))lt lambda lt 2sqrt(2)`