Question

If $PA$ And $PB$ are tangents to the circle with centre $O$ and the angle $APB=60°$

Then Find The Measure Of Angle $OAB$

Answer 1

Find the value of required angle

As given PA and PB are the two tangents to the circle and O be the center of circle.

$\angle APB=60$

Since PA and PB are tangents to the circle from P

$\Rightarrow PA=PB$

$\Rightarrow \angle PAB=\angle PBA$

As given above $\angle APB=60°$

$\angle PAB+\angle PBA=180°-60°=120°$

$2\angle PAB=120°$

$\angle PAB=60°$

$OA$ is the radius and $PA$ is the tangent

$\Rightarrow OA\perp PA$ and $\angle OAP=90°$

$$\begin{gathered} \Rightarrow \angle OAB+\angle PAB=90° \\ \Rightarrow \angle OAB=90°-60° \\ \Rightarrow \angle OAB=30° \end{gathered}$$

Hence the value of $\angle OAB$ is $30°$.