Question

In the given figure, $AT$ is a tangent to the circle with centre $O$ such that $OT=4cm$ and $\angle OTA={30}^o$. Find the length of $AT$.

Answer 1

We know tangent makes ${90}^o$ with centre.

Given $\angle ATO={30}^o$ & $OT=4$cm

$\cos {30}^o=\frac{AT}{OT}=\frac{AT}{4}$

$\frac{\sqrt{3}}{2}=\frac{AT}{4}$

$\Rightarrow AT=4\times \frac{\sqrt{3}}{2}=2\sqrt{3}$.