Question

From any point on the circle $x^2+y^2=a^2$ tangents are drawn to the circle $x^2+y^2=a^2{\sin }^2\alpha$. The angle between them is

• A. $\frac{\alpha }{2}$
• B. $\alpha$
• C. $2\alpha$
• D. None of these

Answer 1

The correct option is C $2\alpha$

Circle $x^2+y^2=a^2$

center $=(0,0)$

radius $=a$

$x^2+y^2=a^2{\sin }^2\alpha$

center $=(0,0)$ radius $=a\sin \alpha$

suppose a point $A$ from where we will draw tangent

Angle between tangent $=2\theta$

Now triangle $AOB$,

$\Rightarrow \sin \theta =\frac{a\sin \alpha }{a}$

$\Rightarrow \sin \theta =\sin \alpha$

$\Rightarrow \theta =\alpha$

so angle between tangent $=2\theta =2\alpha$