In the given figure, AT is a tangent to the circle with centre O,


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) $4 \sqrt{3} \mathrm{~cm}$



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

$O A \perp A T$

So, $\frac{A T}{O T}=\cos 30^{\circ}$

$\Rightarrow \frac{A T}{4}=\frac{\sqrt{3}}{2}$

$\Rightarrow A T=\left(\frac{\sqrt{3}}{2} \times 4\right)$

$\Rightarrow A T=2 \sqrt{3}$


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