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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


Team Careers360 2nd Jan, 2024
Answer (1)
Team Careers360 10th Jan, 2024

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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