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Mathematics · 2025 · 2 marks
CBSE 2025 · Region 2 · Set 1 · Q25
At point A on the diameter AB of a circle of radius 10 cm, tangent XAY is drawn to the circle. Find the length of the chord CD parallel to XY at a…
At point A on the diameter AB of a circle of radius $\displaystyle 10$ cm , tangent XAY is drawn to the circle. Find the length of the chord CD parallel to XY at a distance of $\displaystyle 16$ cm from A.
Marking-scheme solution
\(\displaystyle \mathrm{AP}=16 \mathrm{~cm}\)
\(\displaystyle \therefore \mathrm{OP}=16-10=6 \mathrm{~cm}\)
XY || CD
\(\displaystyle \therefore \angle \mathrm{CPO}=90^{\circ}\)
In right \(\displaystyle \Delta \mathrm{OPC}\),
\[\begin{aligned}
\mathrm{CP} & =\sqrt{(10)^{2}-(6)^{2}}=8 \mathrm{~cm} \\
\mathrm{CD} & =2 \times \mathrm{CP} \\
& =2 \times 8=16 \mathrm{~cm}
\end{aligned}
\]
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CBSE Class 10 Mathematics past-paper question from the 2025 board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.