Question : Two circles of diameters 10 cm and 6 cm have the same centre. A chord of the larger circle is a tangent of the smaller one. The length of the chord is:
Option 1: 4 cm
Option 2: 8 cm
Option 3: 6 cm
Option 4: 10 cm
Correct Answer: 8 cm
Solution :
OE = 3 cm
OC = OD = 5 cm
We know tangent is perpendicular to the radius at its point of contact with the circle.
So, OE $\perp$ CD
Using Pythagoras theorem in $\triangle$ EOC,
CE
2
= OC
2
– OE
2
⇒ CE
2
= 5
2
– 3
2
⇒ CE
2
= 16
⇒ CE = 4 cm
So, CD = 2CE = 2 × 4 = 8 cm
Hence, the correct answer is 8 cm.
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