Question

In the given figure, AT is a tangent to the circle with centre O, such that OT = 4 cm and ∠OTA = 30°. Then, AT = ?


(a) 4 cm
(b) 2 cm
(c) $2\sqrt{3}\mathrm{cm}$
(d) $4\sqrt{3}\mathrm{cm}$

Answer 1

(c) $2\sqrt{3}\mathrm{cm}$

$$\begin{gathered} OA\perp AT \\ \mathrm{So},\frac{AT}{OT}=\cos {30}^0 \\ \Rightarrow \frac{AT}{4}=\frac{\sqrt{3}}{2} \\ \Rightarrow AT=\left(\frac{\sqrt{3}}{2}\times 4\right) \\ \Rightarrow AT=2\sqrt{3} \end{gathered}$$