Question

The angle between the tangents from any point on the circle $x^2+y^2=r^2$ to the circle $x^2+y^2=r^2{\sin }^2\alpha$ is

• A. $\alpha$
• B. $2\alpha$
• C. $\frac{\alpha }{2}$
• D. $4\alpha$

Answer 1

The correct option is B $2\alpha$

From the above figure,

In $△PAO,$

$\sin \theta =\frac{r\sin \alpha }{r}$

or, $\sin \theta =\sin \alpha$

or, $\theta =\alpha$

Therefore, angle between tangents $=2\theta =2\alpha$

Hence, B is the correct option.