Question

In the given figure, PA and PB are two tangents to the circle with centre O. If $\angle APB=50°,$ then what is the measure of $\angle OAB?$

• A. 25°
• B. 30°
• C. 35°
• D. 40°

Answer 1

The correct option is A 25°

We know that tangents from an external point to a circle are equal.

So,
$PA=PB\Rightarrow \angle PAB=\angle PBA...\text{(Angles opposite to equal sides are equal.)}\text{Now in triangle PAB,}\angle PAB+\angle PBA+50°=180°\Rightarrow 2\angle PAB+50°=180°\Rightarrow \angle PAB=65°$

Since AP is a tangent to the circle,
$\angle OAP=90°\Rightarrow \angle OAB+\angle PAB=90°\Rightarrow \angle OAB+65°=90°\Rightarrow \angle OAB=25°$