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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Question : The perpendicular distance from the centre of a circle to the chord is 20 cm. Calculate the chord's length in centimetres if the circle's diameter is 58 cm.
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