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Circles
RD Sharma
CBSE
Grade 10
Question:
If $PA$ and $PB$ are tangents to a circle with centre $O$ from point $P$ such that $PA = 12\text{ cm}$ and $\angle APB = 60^\circ$, find the length of chord $AB$ and distance $OP$.
Step-by-Step Solution
Key Concept: $\Delta PAB$ is equilateral $\Rightarrow AB = 12\text{ cm}$. In right $\Delta OAP$, $\cos 30^\circ = \dfrac{PA}{OP} \Rightarrow \dfrac{\sqrt{3}}{2} = \dfrac{12}{OP} \Rightarrow OP = \dfrac{24}{\sqrt{3}} = 8\sqrt{3}\text{ cm}$.
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Correct Answer:
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