Two concentric circles are of radii $5\text{ cm}$ and $3\text{ cm}$. The length of the chord of the larger circle which touches the smaller circle is:
(a) $8\text{ cm}$
(b) $10\text{ cm}$
(c) $6\text{ cm}$
(d) $4\text{ cm}$
Step-by-Step Solution
Key Concept: Half chord length $= \sqrt{5^2 - 3^2} = 4\text{ cm} \Rightarrow \text{Full chord} = 2 \times 4 = 8\text{ cm}$.
Half chord $= \sqrt{25 - 9} = 4\text{ cm} \Rightarrow \text{Chord} = 2 \times 4 = 8\text{ cm}$. [1.0 Mark]
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🎯 Official CBSE Marking Scheme:
Evaluating chord length $= 8\text{ cm}$: 1.0 Mark
Correct Answer: $8\text{ cm}$