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 \(13\text{ cm}\).

(a) Find angle \(AOB\), giving your answer in radians.

(b) Find the perimeter of the shaded region.

(c) Find the area of the shaded region.