Question : Two concentric circles of radii 15 cm and 13 cm are given. Find the length of the chord of the larger circle which touches the smaller circle.
Option 1: $22\sqrt{7}$
Option 2: $8\sqrt{14}$
Option 3: $4\sqrt{14}$
Option 4: $12\sqrt{7}$
Correct Answer: $4\sqrt{14}$
Solution :
Given: Two concentric circles of radii 15 cm and 13 cm.
We know, that the length of the chord of the larger circle which touches the smaller circle $= 2×\sqrt{R^2-r^2}$, Where $R$ and $r$ are the radii of the bigger and the smaller circle, respectively.
So, the length of the chord of the larger circle which touches the smaller circle
$= 2×\sqrt{15^2-13^2}$
$= 2×\sqrt{56}$
$= 4×\sqrt{14}$ cm
Hence, the correct answer is $4\sqrt{14}$.
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