In a given circle, the chord PQ is of length 18 cm. AB is

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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

1. 27 cm.
2. 30 cm.
3. 28 cm.
4. 25 cm.

Correct Option: B

As per the given figure in question ,

Here , PQ = 18 cm
PM = MQ = 9 cm
OP = OB = r cm
MB = 3 cm
From ∆ OPM,
OP² = PM² + OM²
⇒ r² = 9² + (r – 3)²
⇒ r² = 81 + r² – 6r + 9
⇒ 81 – 6r + 9 = 0
⇒ 6r = 90
⇒ r = 15 cm
∴ AB = 2r = 30 cm