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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