In the given figure, $A B$ is a tangent to the circle centered at $O$. If $O A=6 \mathrm{~cm}$ and $

Question

In the given figure, $A B$ is a tangent to the circle centered at $O$. If $O A=6 \mathrm{~cm}$ and $\angle O A B=30^{\circ}$, then the radius of the circle is :\

Professor PC Thomas Classes · Answer

(a): $\mathrm{As} A B$ is a tangent to a circle, so $\angle O B A=90^{\circ}$. Now, in $	riangle O B A$, $$ \frac{O B}{O A}=\frac{	ext { Perpendicular }}{	ext { Hypotenuse }}=\sin 30^{\circ} $$ $\Rightarrow \frac{O B}{6}=\frac{1}{2} \Rightarrow O B=3 \mathrm{~cm}$\ ∴ Radius of the circle is 3 cm .\