Question

In the given figure , point P is the centre and line AB is the tangent to the circle at T. The radius of the circle is 6 cm. Find PB if $\angle$TPB = 60$°$.

Answer 1

$$\begin{gathered} \mathrm{In}∆\mathrm{PBT},\mathrm{PT}=6\mathrm{cm} \\ \mathrm{Now},\cos \left(\angle \mathrm{P}\right)=\frac{\mathrm{PT}}{\mathrm{PB}} \\ \Rightarrow \cos 60°=\frac{\mathrm{PT}}{\mathrm{PB}} \\ \Rightarrow \frac{1}{2}=\frac{6}{\mathrm{PB}} \\ \therefore \mathrm{PB}=12\mathrm{cm} \end{gathered}$$