2024 IGCSE Additional Mathematics May/June 0606/12 Q6

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

The diagram shows a circle with centre \(O\) and radius \(5\). The points \(A\), \(B\), \(C\) and \(D\) lie on the circumference of the circle. Angle \(DOC=\theta\). Angle \(AOD=\text{angle}\hspace{0.5em}COB=0.5\). The length of the minor arc \(DC\) is \(3.75\).

1. Show that \(\theta=0.75\).[1]
2. Find the perimeter of the shaded region.[5]
3. Find the area of the shaded region.[3]