In the given figure, $T A$ is a tangent to the circle with centre $O$ such that $O T=4 \mathrm{~cm},

Question

In the given figure, $T A$ is a tangent to the circle with centre $O$ such that $O T=4 \mathrm{~cm}, \angle O T A=30^{\circ}$, then length of TA is\

Professor PC Thomas Classes · Answer

(a): Draw $O A \perp T A$.
 In $	riangle \mathrm{OTA}, \angle \mathrm{OAT}=90^{\circ}(\because$ Tangent to a circle is perpendicular to the radius passing through the point of contact)\ and $\angle O T A=30^{\circ}$\ $	herefore \quad \frac{T A}{O T}=\cos 30^{\circ} \Rightarrow T A=4 \cos 30^{\circ}=4 	imes \frac{\sqrt{3}}{2}$\ $\Rightarrow T A=2 \sqrt{3} \mathrm{~cm}$\