PQRS is a cyclic quadrilateral. The bisectors of the angles

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PQRS is a cyclic quadrilateral. The bisectors of the angles ∠P and ∠R meet the circle ABCD at A and B respectively. If the radius of the circle be r units, then AB = ?

1. r
2. 2r
3. 2 r
  3
4. 3 r
  2

Correct Option: B

As per the above given question , we draw a figure of a cyclic quadrilateral PQRS and the bisectors of the angles ∠P and ∠R meet the circle ABCD at A and B respectively

PQRS is a cyclic quadrilateral.
∠P + ∠R = 180°

⇒	1	∠P +	1	∠R = 90°
	2		2

⇒ ∠APS + ∠BRS = 90° ....(i)
But ∠BRS and ∠BPS are angles in the same segment with chord BS.
∴ ∠BRS = ∠BPS .....(ii)
∴ ∠APS + ∠BPS = 90°
⇒ ∠APB = 90°
∴ AB is the diameter.