2024 IGCSE Additional Mathematics October/November 0606/12 Q3

In this question, all lengths are in centimetres and all angles are in radians.

The diagram shows a circle with centre \(O\) and radius \(12\), and a circle with centre \(C\) and radius \(5\). The circles intersect at the points \(A\) and \(B\), such that \(OA\) and \(OB\) are tangents to the circle with centre \(C\).

1. Show that the obtuse angle \(ACB\) is \(2.35\) radians, correct to 2 decimal places.[2]
2. Find the perimeter of the shaded region.[2]
3. Find the area of the shaded region.[3]