Question : The circumference of a circle is $58 \pi$ cm. There is a chord XY of length 42 cm in this circle. What is the distance of this chord XY from the centre?
Option 1: 32 cm
Option 2: 20 cm
Option 3: 28 cm
Option 4: 24 cm
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Correct Answer: 20 cm
Solution :
Circumference = $2\pi r$
⇒ $58\pi=2\pi r$
⇒ $r = 29$ cm
In triangle XOP,
XP = 21 cm
OX = 29 cm
Apply Pythagoras' theorem, we get
$OX^2 = OP^2 + XP^2$
$29^2= OP^2 + 21^2$
⇒ $OP^2= 841 - 441$
⇒ $OP^2 = 400$
⇒ $OP = 20$ cm
Hence, the correct answer is 20 cm.
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