Question : A chord of length 24 cm is at a distance of 5 cm from the centre of the circle. The radius of the circle is:
Option 1: 13 cm
Option 2: 12 cm
Option 3: 16 cm
Option 4: 15 cm
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Correct Answer: 13 cm
Solution : Let O be the centre of the circle. Let AB be the chord of length 24 cm Let OD be perpendicular from the centre to the chord AB of length 5 cm. We know the perpendicular from the centre to a chord bisects the chord. So, AD = BD = 12 units Applying Pythagoras theorem in triangle OBD, OB2 = OD2 + DB2 ⇒ OB2 = 52 + 122 ⇒ OB2 = 169 ⇒ OB = 13 Hence, the correct answer is 13 cm.
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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
Question : The radius of a circle is 10 cm. The distance of chord PQ from the centre is 8 cm. What is the length of chord PQ?
Option 1: 16 cm
Option 2: 15 cm
Option 3: 12 cm
Option 4: 14 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 : 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 : A chord is drawn in a circle of radius 10 cm, if the distance of the chord from the centre is 6 cm, then the length of the chord (in cm) is:
Option 1: 10
Option 2: 12
Option 3: 16
Option 4: 8
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