Question

A tangent PA is drawn from an external point P to a circle of radius $3\sqrt{2}$ cm such that the distance of the point P from O is 6 cm as shown in the figure. The value of $\angle APO$ is

• A. ${30}^{\circ }$
• B. ${45}^{\circ }$
• C. ${60}^{\circ }$
• D. ${75}^{\circ }$

Answer 1

The correct option is B ${45}^{\circ }$

Tangent and radius are perpendicular at the point of contact.

Let $\angle APO=\theta$. Then in triangle $OAP$, we have:

$\sin \theta =\frac{OA}{OP}=\frac{1}{\sqrt{2}}\Rightarrow \theta ={45}^o$.

So option B is the right answer.