Question

If PA and PB are tangents to the circle with centre O such that $\angle$APB = 50⁰, then $\angle$OAB is equal to

(a) 25⁰ (b) 30⁰ (c) 40⁰ (d) 50⁰

Answer 1

In quadrilateral APBO,
$\angle APB=50°$
$$\begin{gathered} \angle OAP+\angle APB+\angle PBO+\angle AOB=360° \\ \Rightarrow 90°+90°+50°+\angle AOB=360° \\ \Rightarrow \angle AOB=130° \end{gathered}$$
In ∆AOB,
Let $\angle OAB=\angle OBA=x$ (OA = OB as they are radii)
$$\begin{gathered} \angle AOB+\angle OBA+\angle OAB=180° \\ \Rightarrow 130°+2x=180 \\ \Rightarrow x=25° \end{gathered}$$
Hence, the correct answer is option (a).