Angle between Pair of Tangents

Q.

The range of values of 'a' such that the angle $\theta$ between the pair of tangents drawn from (a, 0) to the circle $x^2+y^2=1$ satisfies $\frac{\pi }{2}<\theta <\pi$, is

1. $(1,2)$

2. $(1,\sqrt{2})$
   

3. $(-\sqrt{2},-1)$
   

4. $(-\sqrt{2},-1)\cup (1,\sqrt{2})$

Q. The range of values of $a$ such that the angle $\theta$ between the pair of tangents drawn from $(a,0)$ to the circle $x^2+y^2=1$ satisfies $\frac{\pi }{2}<\theta <\pi$, lies in

1. $(-1,0)\cup (\sqrt{2},5)$
2. $(-1,0)\cup (1,\sqrt{2})$
3. $(-\sqrt{2},-1)\cup (0,\sqrt{2})$
4. $(-\sqrt{2},-1)\cup (1,\sqrt{2})$

Q. The angle between the tangents from $(\alpha ,\beta )$ to the circle $x^2+y^2=a^2$, is

1. $ta{n}^{-1}\frac{a}{\sqrt{{\alpha }^2+{\beta }^2-a^2}}$
2. $ta{n}^{-1}\frac{\sqrt{{\alpha }^2+{\beta }^2-a^2}}{a}$
3. $2ta{n}^{-1}\frac{a}{\sqrt{{\alpha }^2+{\beta }^2-a^2}}$
4. $Noneofthese$