Question : Two concentric circles are of radii 10 cm and 6 cm. Find the length of the chord of the larger circle which touches the smaller circle.
Option 1: 8 cm
Option 2: 16 cm
Option 3: 12 cm
Option 4: 9 cm
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Correct Answer: 16 cm
Solution :
We have, OB = 10 cm and OD = 6 cm Radius perpendicular to the tangent. $\angle ODB$ = 90º Using Pythagoras' theorem in $\triangle ODB$ OB 2 = OD 2 + BD 2 ⇒ 10 2 = 6 2 + BD 2 ⇒ BD 2 = 64 ⇒ BD = 8 cm As, AB = 2BD AB = 2 × 8 = 16 cm Hence, the correct answer is 16 cm.
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