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Circles
RD Sharma
CBSE
Grade 10

Question:

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: $\tan 30^\circ = \dfrac{r}{\text{length}} \Rightarrow \dfrac{1}{\sqrt{3}} = \dfrac{3}{l} \Rightarrow l = 3\sqrt{3}\text{ cm}$.
$\tan 30^\circ = \dfrac{3}{l} \Rightarrow \dfrac{1}{\sqrt{3}} = \dfrac{3}{l} \Rightarrow l = 3\sqrt{3}\text{ cm}$. [1.0 Mark]

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🎯 Official CBSE Marking Scheme:
Calculating tangent length $= 3\sqrt{3}\text{ cm}$: 1.0 Mark

Correct Answer: $3\sqrt{3}\text{ cm}$
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