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) $4 \sqrt{3} \mathrm{~cm}$
Solution:
(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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