A circle with centre \(O\) has diameter \(AB\). A line segment is drawn from a point \(C\) on the circumference of the circle to \(D\) on \(OB\) such that \(CD\perp OB\) and \(CD=2\) units. Two circles are drawn on \(AB\). One has diameter \(AD\) and the other has diameter \(DB\).
Determine the area of the shaded region. That is, determine the area inside the circle centred at \(O\) but outside of the circle with diameter \(AD\) and outside of the circle with diameter \(DB\).
Note: In solving this problem, it may be helpful to use the fact that the angle inscribed in a circle by the diameter is \(90\degree\). For example, in the following diagram, \(PQ\) is a diameter and \(\angle PRQ\) is inscribed in the circle by diameter \(PQ\). Therefore, \(\angle PRQ=90\degree.\)
