Question : The radius of a circle is 10 cm. The distance of chord PQ from the centre is 8 cm. What is the length of chord PQ?
Option 1: 16 cm
Option 2: 15 cm
Option 3: 12 cm
Option 4: 14 cm
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Correct Answer: 12 cm
Solution :
Given: The radius of a circle = PA = 10 cm
The distance of chord PQ from the centre = OA = 8 cm
Using Pythagoras's theorem,
$PA^2=OP^2-OA^2$
⇒ $PA^2=10^2-8^2$
⇒ $PA^2=100-64$
⇒ $PA^2=36$
⇒ $PA=6$
$\therefore PQ = 2\times PA=2\times6=12\ \text{cm}$
Hence, the correct answer is 12 cm.
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