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 \(D O C=\theta\). Angle \(A O D=\) angle \(C O B=0.5\). The length of the minor \(\operatorname{arc} D C\) is 3.75 . (a) Show that \(\theta=0.75\).

(b) Find the perimeter of the shaded region.

(c) Find the area of the shaded region.