Question : Two circles of radii 12 cm and 13 cm are concentric. The length of the chord of the larger circle which touches the smaller circle is:
Option 1: 8 cm
Option 2: 18 cm
Option 3: 10 cm
Option 4: 12 cm
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Correct Answer: 10 cm
Solution :
Let O be the centre of the circle. OA = 13 cm and OM = 12 cm.
Let AB be the chord of the smaller circle which is tangent to a smaller circle.
Since the tangent is perpendicular to the radius at its point of contact, angle OMA is a right angle.
By Pythagoras theorem,
OA
2
= AM
2
+ OM
2
⇒ 13
2
= AM
2
+ 12
2
⇒ AM
2
= 25
⇒ AM = 5 cm
Also, perpendicular from the centre to a chord bisects the chord.
AB = 2 × AM = 2 × 5 = 10 cm
Hence, the correct answer is 10 cm.
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