In figure, AT is a tangent to the circle


In figure, $\mathrm{AT}$ is a tangent to the circle with centre 0 such that $\mathrm{OT}=4 \mathrm{~cm}$ and $\angle \mathrm{OTA}=30^{\circ}$. Then, $\mathrm{AT}$ is equal to

(a) 4 cm              

(b) 2 cm                  

(c) 2√3 cm                    

(d) 4√3 cm


(c) Join OA

We know that, the tangent at any point of a circle is perpendicular to the radius through the point of contact.

$\therefore \quad \angle O A T=90^{\circ}$

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

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

$\Rightarrow$ $A T=2 \sqrt{3} \mathrm{~cm}$


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