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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