2026 IGCSE Additional Mathematics May/June 0606/12 Q6

In this question lengths are in centimetres.

The diagram shows a circle with centre \(O\) and radius \(r\).

Points \(A\), \(B\) and \(C\) are on the circumference of the circle.

Angle \(AOB=\alpha\) radians.

1. The perimeter of the shaded sector is equal to the length of the major arc, \(ACB\).
   Find the exact value of \(\alpha\).[4]
2. The area of the shaded sector is \(18(\pi^2-1)\).
   Find the exact value of \(r\).
   Simplify your answer.[4]