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Circles
NCERT Exemplar Ch 09
CBSE_NCERT_EXEMPLAR_CH09
Grade 10

Question:

At one end $A$ of a diameter $AB$ of a circle of radius $5\text{ cm}$, tangent $XAY$ is drawn to the circle. The length of the chord $CD$ parallel to $XY$ and at a distance $8\text{ cm}$ from $A$ is:

$4\text{ cm}$
$5\text{ cm}$
$6\text{ cm}$
$8\text{ cm}$

Step-by-Step Solution

Key Concept: Center $O$ is at distance $5\text{ cm}$ from $A$. Chord $CD$ at distance $8\text{ cm}$ from $A$ is at distance $|8 - 5| = 3\text{ cm}$ from $O$.
Stepwise Solution:

Distance of chord from center $O = 8 - 5 = 3\text{ cm}$. [0.5 Mark]

Half-chord $= \sqrt{5^2 - 3^2} = \sqrt{16} = 4\text{ cm}$. Full chord $CD = 2 \times 4 = 8\text{ cm}$. [0.5 Mark]

Marking Scheme:

• Distance from center $= 3\text{ cm}$: 0.5 Mark
• Length of chord $= 2 \times 4 = 8\text{ cm}$: 0.5 Mark

Correct Answer: $8\text{ cm}$
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