2025 IGCSE Additional Mathematics October/November 0606/23 Q8

In this question the units are metres.

The diagram shows a circle, centre \(O\) and radius 2.

The chord \(AB\) has length \(2\sqrt3\).

The point \(Q\) lies on the circle such that \(AQ=BQ\).

The arc \(APB\) is part of a circle, centre \(Q\).

1. Find the exact value of angle \(AQB\) in radians.[2]
2. Hence find the area of the shaded region. Give your answer in terms of \(\pi\).[6]