Question : AB is a chord of a circle having a radius of 1.7 cm. If the distance of this chord AB from the centre of the circle is 0.8 cm, then what is the length (in cm) of the chord AB?
Option 1: 4
Option 2: 1
Option 3: 3
Option 4: 2
Correct Answer: 3
Solution :
OB = 1.7 cm
OC = 0.8 cm
In $\triangle$ OCB,
$OB^2 = OC^2 + CB^2$
⇒ $1.7^2 = 0.8^2 + CB^2$
⇒ $2.89 = 0.64 + CB^2$
⇒ $CB^2 = 2.89 – 0.64 = 2.25$
$\therefore$ $CB = 1.5$ cm
AB = 2 × CB = 2 × 1.5 = 3 cm
Hence, the correct answer is 3 cm.
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