3.29: Chord with an arc from an external centre on the circle

0606/23/O/N/25 — Question 8 · 8 marks

3.29 diagram
In this question the units are metres.
The diagram shows a circle, centre OO and radius 22.
The chord ABAB has length 232\sqrt{3}.
The point QQ lies on the circle such that AQ=BQAQ = BQ.
The arc APBAPB is part of a circle, centre QQ.
(a)
Find the exact value of angle AQBAQB in radians.
[2]
(b)
Hence find the area of the shaded region. Give your answer in terms of π\pi.
[6]