Question : Two concentric circles are drawn with radii 12 cm and 13 cm. What will be the length of any chord of the larger circle that is tangent to the smaller circle?
Option 1: 5 cm
Option 2: 8 cm
Option 3: 10 cm
Option 4: 25 cm
Correct Answer: 10 cm
Solution :
OE = 12 cm
OC = OD = 13 cm
We know that the tangent is perpendicular to the radius at its point of contact.
OE $\perp$ CD
Using Pythagoras theorem in $\triangle$ EOC,
CE
2
= OC
2
– OE
2
⇒ CE
2
= 13
2
– 12
2
⇒ CE
2
= 25
⇒ CE = 5 cm
CD = 2CE = 2 × 5 = 10 cm
Hence, the correct answer is 10 cm.
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