A circle, centre \(O\) and radius \(r\) cm, has a sector \(OAB\) of fixed area \(10\text{ cm}^2\). Angle \(AOB\) is \(\theta\) radians and the perimeter is \(P\) cm.

(a) Find \(P\) in terms of \(r\).

(b) Find \(r\) for which \(P\) has a stationary value.

(c) Determine the nature of this stationary value.

(d) Find \(\theta\) at this stationary value.