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Circles
RD Sharma
CBSE
Grade 10
Question:
At one end $A$ of a diameter $AB$ of a circle of radius $5\text{ cm}$, tangent $XAY$ is drawn. The length of the chord $CD$ parallel to $XY$ at a distance of $8\text{ cm}$ from $A$ is: (a) $8\text{ cm}$ (b) $4\text{ cm}$ (c) $6\text{ cm}$ (d) $5\text{ cm}$
Step-by-Step Solution
Key Concept: Distance of $CD$ from centre $O = 8 - 5 = 3\text{ cm}$. Half chord $= \sqrt{5^2 - 3^2} = 4\text{ cm} \Rightarrow CD = 2 \times 4 = 8\text{ cm}$.
Distance from centre $= 8 - 5 = 3\text{ cm}$. Half chord $= \sqrt{25 - 9} = 4\text{ cm} \Rightarrow CD = 8\text{ cm}$. [1.0 Mark]
--- 🎯 Official CBSE Marking Scheme: Calculating chord length $= 8\text{ cm}$: 1.0 Mark
Correct Answer:$8\text{ cm}$
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