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
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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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