Circles
NCERT Exemplar Ch 09
CBSE_NCERT_EXEMPLAR_CH09
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:
$r\sqrt{3}$
$2r$
$\dfrac{r\sqrt{3}}{2}$
$\dfrac{r}{\sqrt{3}}$
Step-by-Step Solution
Key Concept: In right $\Delta OAP$, $\angle APO = 30^\circ$. $\sin 30^\circ = \dfrac{r}{OP} = \dfrac{1}{2} \Rightarrow OP = 2r$.
Stepwise Solution:
$\angle APO = 30^\circ$. $\sin 30^\circ = \dfrac{OA}{OP} \Rightarrow \dfrac{1}{2} = \dfrac{r}{OP} \Rightarrow OP = 2r$. [1.0 Mark]
Marking Scheme:
• Applying $\sin 30^\circ = r/OP \Rightarrow OP = 2r$: 1.0 Mark
Correct Answer: $2r$
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