Question : Two concentric circles are drawn with radii of 20 cm and 16 cm. What will be the length of a chord of the larger circle which is tangent to the smaller circle?
Option 1: 34 cm
Option 2: 24 cm
Option 3: 48 cm
Option 4: 12 cm
Correct Answer: 24 cm
Solution :
As BOC is a right-angled triangle at C,
Applying Pythagoras theorem,
⇒ $(BO)^2 = (CO)^2 + (BC)^2$
⇒ $(20)^2 = (16)^2 + (BC)^2$
⇒ $400 = 256 + BC^2$
⇒ $BC = \sqrt{\text{400 – 256}}$
⇒ $BC = \sqrt{144}$
⇒ $BC = 12$
$\therefore AB = 12×2=24$ cm
Hence, the correct answer is 24 cm.
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