Question

In figure, AT is a tangent to the circle with centre O such that OT = 4 cm and $\angle OTA={30}^{\circ }$ . Then , AT is equal to

Answer 1

Join OA.
We know that, the tangent at any point of a circle is perpendicular to the radius trough the point of contact.
$\therefore \angle OAT={90}^{\circ }In\Delta OAT,Cos{30}^{\circ }=\frac{AT}{OT}\Rightarrow \frac{\sqrt{3}}{2}=\frac{AT}{4}\Rightarrow AT=2\sqrt{3}cm$