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
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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