If radii of two concentric circles are $4\text{ cm}$ and $5\text{ cm}$, then the length of each chord of one circle which is tangent to the other circle is:
(a) $3\text{ cm}$
(b) $6\text{ cm}$
(c) $9\text{ cm}$
(d) $1\text{ cm}$
Step-by-Step Solution
Key Concept: The radius to the point of contact is perpendicular to the tangent chord and bisects it. Use Pythagoras: half-length $= \sqrt{5^2 - 4^2} = 3\text{ cm}$.
Half-chord $= \sqrt{5^2 - 4^2} = \sqrt{25 - 16} = 3\text{ cm}$. [0.5 Mark]
Total length of chord $= 2 \times 3 = 6\text{ cm}$. [0.5 Mark]
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🎯 Official CBSE Marking Scheme:
Applying Pythagoras to find half-chord $= 3\text{ cm}$: 0.5 Mark
Doubling to get full chord length $= 6\text{ cm}$: 0.5 Mark
Correct Answer: $6\text{ cm}$