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.
Option 1: 42
Option 2: 21
Option 3: 56
Option 4: 28
Question : A chord of length 48 cm is at a distance of 7 cm from the centre of the circle. What is the length of the chord of the same circle which is at a distance of 15 cm from the centre of the circle?
Option 1: 40 cm
Option 2: 45 cm
Option 3: 35 cm
Option 4: 42 cm
Question : The sum of the angles made by a chord XY at the centre and on the circumference of the circle is 270°. If the radius of this circle is 24 cm, then what will be the length of this chord?
Option 1: 60 cm
Option 2: 12 cm
Option 3: 36 cm
Option 4: 48 cm
Question : A chord of length 40 cm is at a distance of 15 cm from the centre. What is the length of the chord of the same circle which is at a distance of 20 cm from the centre of the circle?
Option 1: 15 cm
Option 2: 25 cm
Option 3: 45 cm
Option 4: 30 cm
Question : In a circle, the length of a chord is 30 cm. The perpendicular distance of the chord from the centre of the circle is 8 cm. Find the diameter of the circle.
Option 1: 28 cm
Option 2: 34 cm
Option 3: 17 cm
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