If two tangents inclined at an angle of $60^\circ$ are drawn to a circle of radius $3\text{ cm}$, then length of each tangent is equal to:
(a) $\dfrac{3}{2}\sqrt{3}\text{ cm}$
(b) $6\text{ cm}$
(c) $3\sqrt{3}\text{ cm}$
(d) $3\text{ cm}$
Step-by-Step Solution
Key Concept: In right $\Delta OAP$, $\angle APO = 30^\circ$. $\tan 30^\circ = \dfrac{r}{AP} = \dfrac{3}{AP} = \dfrac{1}{\sqrt{3}} \Rightarrow AP = 3\sqrt{3}\text{ cm}$.
$\tan 30^\circ = \dfrac{3}{AP} \Rightarrow \dfrac{1}{\sqrt{3}} = \dfrac{3}{AP} \Rightarrow AP = 3\sqrt{3}\text{ cm}$. [1.0 Mark]
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🎯 Official CBSE Marking Scheme:
Applying $\tan 30^\circ = 3/AP \Rightarrow AP = 3\sqrt{3}\text{ cm}$: 1.0 Mark
Correct Answer: $3\sqrt{3}\text{ cm}$