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
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Correct Answer: 42
Solution : Given: Diameter, AB = $58$ cm So, Radius = $\frac{58}{2}=29$ cm CD is the chord. Its distance from the centre, ON is $20$ cm. CD = $2$ × CN Join OC. OC is the radius. From $\triangle$OCN, OC2 = ON2 + CN2 ⇒ $29^2=20^2$+CN2 ⇒ CN2= $841-400$ ⇒ CN = $21$ cm So, CD = $2 × 21 = 42$ cm So, the length of the chord is 42 cm. Hence, the correct answer is 42.
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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
Option 4: 30 cm
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
Question : The length of the chord of a circle is 8 cm and the perpendicular distance between the centre and the chord is 3 cm, then the diameter of the circle is equal to:
Option 1: 5 cm
Option 2: 10 cm
Option 3: 3 cm
Option 4: 7 cm
Question : The distance of a chord OP from the centre of a circle is 6 cm. If the diameter of this circle is 20 cm, then what will be the sum of the radius and length of chord OP?
Option 1: 18 cm
Option 2: 26 cm
Option 3: 16 cm
Option 4: 20 cm
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
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