Question : In a given circle, the chord PQ is of length 18 cm. AB is the perpendicular bisector of PQ at M. If MB = 3 cm, then the length of AB is:
Option 1: 27 cm
Option 2: 30 cm
Option 3: 28 cm
Option 4: 25 cm
Correct Answer: 30 cm
Solution : Given, PQ = 18 cm $\therefore$ PM = MQ = 9 cm Let OP = OB = r cm MB = 3 cm In $\triangle$ OPM, OP 2 = PM 2 + OM 2 ⇒ r 2 = 9 2 + (r – 3) 2 ⇒ r 2 = 81 + r 2 – 6r + 9 ⇒ 6r = 90 $\therefore$ r = 15 cm $\therefore$ AB = 2r = 2 × 15 = 30 cm Hence, the correct answer is 30 cm.
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Question : In the given figure, point O is the centre of a circle of radius 13 cm and AB is a chord perpendicular to OD. If CD = 8 cm, what is the length (in cm) of AB?
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Question : AB is a chord in a circle of radius 13 cm. From centre O, a perpendicular is drawn through AB intersecting AB at point C. The length of OC is 5 cm. What is the length of AB?
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