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Circles
NCERT Exemplar
CBSE
Grade 10
Question:
If the angle between two tangents drawn from a point $P$ to a circle of radius $r$ and center $O$ is $60^\circ$, then $OP$ is equal to: (a) $r\sqrt{3}$ (b) $2r$ (c) $\dfrac{r\sqrt{3}}{2}$ (d) $\dfrac{r}{\sqrt{3}}$
Step-by-Step Solution
Key Concept: In right $\Delta OAP$, $\angle APO = 30^\circ$. $\sin 30^\circ = \dfrac{r}{OP} = \dfrac{1}{2} \Rightarrow OP = 2r$.
$\angle APO = 30^\circ$. $\sin 30^\circ = \dfrac{OA}{OP} \Rightarrow \dfrac{1}{2} = \dfrac{r}{OP} \Rightarrow OP = 2r$. [1.0 Mark]
--- 🎯 Official CBSE Marking Scheme: Applying $\sin 30^\circ = r/OP \Rightarrow OP = 2r$: 1.0 Mark
Correct Answer:$2r$
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