Question

Question 6
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
(A) 4 cm
(B) 2 cm
(C) 2 $\sqrt{3}$ cm
(D) 4 $\sqrt{3}$ cm

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.

$\therefore \angle OAT={90}^{\circ }In\Delta OAT,Cos{30}^{\circ }=\frac{AT}{OT}\Rightarrow \frac{\sqrt{3}}{2}=\frac{AT}{4}\Rightarrow AT=2\sqrt{3}cm$