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
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Correct Answer: 34 cm
Solution : Let AB be the chord and O be the center of the circle. Also, OP is perpendicular to AB In $\triangle$ OPB, OB2 = PB2 + OP2 ⇒ OB2 = 152 + 82 ⇒ OB2 = 225 + 64 ⇒ OB2 = 289 ⇒ OB = $\sqrt{289}$ ⇒ OB = 17 cm Diameter = 2 × OB = 2 × 17 = 34 cm ∴ The diameter of the circle is 34 cm. Hence, the correct answer is 34 cm.
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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 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 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
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 : Half of the length of a chord of a circle is 12 cm and the perpendicular distance between the centre and the chord is 5 cm. The radius of the circle is:
Option 1: 12 cm
Option 2: 13 cm
Option 3: 10 cm
Option 4: 24 cm
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