Question

In the given figure, PA and PB are tangents, such that PA = 9 cm and ∠APB = 60°. Find the length of chord AB.

Answer 1

The lengths of tangents drawn from a point to a circle are equal.
So, PA= PB.
$$\begin{gathered} Suppose,\mathrm{\angle }PAB=\mathrm{\angle }PBA=x \\ \mathrm{Then},\text{in}∆PAB: \\ \mathrm{\angle }PAB+\mathrm{\angle }PBA+\mathrm{\angle }APB={180}^0 \\ \Rightarrow x+x+{60}^0={180}^0 \\ \Rightarrow 2x={120}^0 \\ \Rightarrow x=\frac{{120}^0}{2}={60}^0 \\ \therefore \mathrm{The}\mathrm{}\mathrm{angles}\mathrm{}\mathrm{of}∆PAB\mathrm{are}{60}^0. \\ \therefore \mathrm{It}\mathrm{}\mathrm{is}\mathrm{}\mathrm{an}\mathrm{}\mathrm{equilateral}\mathrm{}\mathrm{triangle}. \\ \therefore AB=PA=PB=9\mathrm{cm} \end{gathered}$$
The length of chord AB is 9 cm.