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Mathematics · 2023 · 3 marks
CBSE 2023 · Region 4 · Set 1 · Q30
Two concentric circles are of radii 5 cm and 3 cm. Find the length of the chord of the larger circle which touches the smaller circle.
Two concentric circles are of radii $\displaystyle 5$ cm and $\displaystyle 3$ cm. Find the length of the chord of the larger circle which touches the smaller circle.
Marking-scheme solution
AB is the chord of larger circle touching the smaller circle at P.
\[\mathrm{OA}=5 \mathrm{~cm}, \mathrm{OP}=3 \mathrm{~cm}
\]
To find AB
\(\displaystyle \mathrm{OP} \perp \mathrm{AB}\) (radius ⟂ tangent)
AB is the chord of larger circle and \(\displaystyle \mathrm{OP} \perp \mathrm{AB}\)
\[\therefore \mathrm{AP}=\mathrm{PB}
\]
In right-angled \(\displaystyle \triangle \mathrm{AOP}, \mathrm{AP}^{2}=5^{2}-3^{2}=16\)
\[\text { AP }=4 \mathrm{~cm}
\]
\(\displaystyle \therefore \mathrm{AB}=2 \mathrm{AP}=8 \mathrm{~cm}\)
\[\mathrm{OA}=5 \mathrm{~cm}, \mathrm{OP}=3 \mathrm{~cm}
\]
To find AB
\(\displaystyle \mathrm{OP} \perp \mathrm{AB}\) (radius ⟂ tangent)
AB is the chord of larger circle and \(\displaystyle \mathrm{OP} \perp \mathrm{AB}\)
\[\therefore \mathrm{AP}=\mathrm{PB}
\]
In right-angled \(\displaystyle \triangle \mathrm{AOP}, \mathrm{AP}^{2}=5^{2}-3^{2}=16\)
\[\text { AP }=4 \mathrm{~cm}
\]
\(\displaystyle \therefore \mathrm{AB}=2 \mathrm{AP}=8 \mathrm{~cm}\)More from Circles
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CBSE Class 10 Mathematics past-paper question from the 2023 board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.