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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


Team Careers360 19th Jan, 2024
Answer (1)
Team Careers360 24th Jan, 2024

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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