2025 IGCSE Additional Mathematics February/March 0606/22 Q1

The diagram shows a circle with centre \(O\) and radius \(5\text{ cm}\).

The point \(A\) lies on the circle.

The point \(B\) is such that the line \(AB\) is a tangent to the circle.

\(OB\) has length \(13\text{ cm}\).

1. Find angle \(AOB\), giving your answer in radians.[2]
2. Find the perimeter of the shaded region.[3]
3. Find the area of the shaded region.[3]