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Circles
RD Sharma
CBSE
Grade 10

Question:

In a circle of radius $5\text{ cm}$, two parallel chords of lengths $6\text{ cm}$ and $8\text{ cm}$ are drawn on opposite sides of the centre. Find the distance between the two chords.

Step-by-Step Solution

Key Concept: Distance of $6\text{ cm}$ chord from centre $= \sqrt{5^2 - 3^2} = 4\text{ cm}$. Distance of $8\text{ cm}$ chord from centre $= \sqrt{5^2 - 4^2} = 3\text{ cm}$. Total distance $= 4 + 3 = 7\text{ cm}$.
Distance of $6\text{ cm}$ chord $= \sqrt{25 - 9} = 4\text{ cm}$. [1.0 Mark]
Distance of $8\text{ cm}$ chord $= \sqrt{25 - 16} = 3\text{ cm}$. [1.0 Mark]
Total distance $= 4 + 3 = 7\text{ cm}$. [1.0 Mark]

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🎯 Official CBSE Marking Scheme:
Finding distance of 6 cm chord $= 4\text{ cm}$: 1.0 Mark
Finding distance of 8 cm chord $= 3\text{ cm}$: 1.0 Mark
Evaluating total distance $= 7\text{ cm}$: 1.0 Mark

Correct Answer:
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