In the given figure, $A C$ and $A B$ are tangents to a circle centered at $O$. If $\angle C O D=120^

Question

In the given figure, $A C$ and $A B$ are tangents to a circle centered at $O$. If $\angle C O D=120^{\circ}$, then $\angle B A O$ is equal to :\

Professor PC Thomas Classes · Answer

(a): $\angle A O C+\angle C O D=180^{\circ}$ (Linear pair)\ $\Rightarrow \angle A O C=180^{\circ}-120^{\circ}=60^{\circ}$ $$ \left(\because \angle C O D=120^{\circ}ight) $$ $\Rightarrow \angle A C O=90^{\circ} \quad$ (Tangent at any point of a circle is perpendicular to the radius through the point of contact)\ In $	riangle A C O$,\ $\angle A C O+\angle C O A+\angle O A C=180^{\circ}$\ $\Rightarrow \angle \mathrm{OAC}=180^{\circ}-90^{\circ}-60^{\circ}=30^{\circ}$\ $	herefore \quad \angle B A O=\angle O A C=30^{\circ}$ $$ (\because 	riangle A B O \cong 	riangle A C O) $$