Question : A chord is drawn in a circle of radius 10 cm, if the distance of the chord from the centre is 6 cm, then the length of the chord (in cm) is:
Option 1: 10
Option 2: 12
Option 3: 16
Option 4: 8
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Correct Answer: 16
Solution :
In $\triangle AOS$, AO is the radius.
⇒ $AO = 10$ cm
It is right-angled at S,
Applying Pythagoras theorem, we get,
$AO^2=OS^2+AS^2$
⇒ $10^2=6^2+AS^2$
⇒ $100-36=AS^2$
⇒ $AS^2 = 64$
⇒ $AS=8 $ cm
Now, $AS = \frac{1}{2}×$ Length of the chord
⇒ Length of Chord $= 2\times 8=16$ cm
Hence, the correct answer is 16.
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