In the given figure, $PQ$ and $PR$ are tangents to a circle with ce...

Question

In the given figure, $PQ$ and $PR$ are tangents to a circle with centre $O$ and radius $3$ cm. If $\angle QPR = 60^\circ$, then the length of each tangent is :

Accepted Answer

Step 1: $OP$ bisects $\angle QPR$, so $\angle OPQ = \dfrac{60^\circ}{2} = 30^\circ$.
Step 2: Radius $\perp$ tangent, so $\angle OQP = 90^\circ$.
Step 3: In right $	riangle OQP$,
$$	an 30^\circ = \frac{OQ}{PQ} = \frac{3}{PQ}$$
Step 4: $$\frac{1}{\sqrt{3}} = \frac{3}{PQ} \Rightarrow PQ = 3\sqrt{3}\ 	ext{cm}$$

Correct option : (A)

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