A piece of wire of length 50 cm is bent to form the perimeter of a sector POQ of a circle. The radius of the circle is r cm and the angle POQ is \(\theta\) radians (see diagram).

(i) Express \(\theta\) in terms of \(r\) and show that the area, \(A \text{ cm}^2\), of the sector is given by \(A = 25r - r^2\).

(ii) Given that \(r\) can vary, find the stationary value of \(A\) and determine its nature.