In the given figure, TA is a tangent to the circle with centre O such that $OT = 4$ cm, $\angle OTA = 30°$, then length of TA is:

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In the given figure, TA is a tangent to the circle with centre O such that $OT = 4$ cm, $\angle OTA = 30°$, then length of TA is:

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Accepted Answer

Step 1: $\angle OAT = 90°$ (radius $\perp$ tangent). In $	riangle OAT$: $\cos 30° = \frac{TA}{OT} \Rightarrow \frac{\sqrt{3}}{2} = \frac{TA}{4} \Rightarrow TA = 2\sqrt{3}$ cm

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