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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


Team Careers360 9th Jan, 2024
Answer (1)
Team Careers360 20th Jan, 2024

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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