If $PA$ and $PB$ are tangents to a circle from point $P$ such that $PA = 10\text{ cm}$ and $\angle APB = 60^\circ$, then length of chord $AB$ is:
(a) $10\text{ cm}$
(b) $5\text{ cm}$
(c) $5\sqrt{3}\text{ cm}$
(d) $20\text{ cm}$
Step-by-Step Solution
Key Concept: Since $PA = PB = 10\text{ cm}$ and $\angle APB = 60^\circ$, $\Delta PAB$ is an equilateral triangle $\Rightarrow AB = 10\text{ cm}$.
$\Delta PAB$ is equilateral $\Rightarrow AB = PA = 10\text{ cm}$. [1.0 Mark]
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🎯 Official CBSE Marking Scheme:
Deducing equilateral triangle $AB = 10\text{ cm}$: 1.0 Mark
Correct Answer: $10\text{ cm}$