Radius and angle of a sector from its area and perimeter in degrees, then the inner radius of an annular sector

A paper fan is in the shape of the sector \(OAB\) of a circle with centre \(O\) and radius \(R\text{ cm}\), where \(A\hat{O}B=\theta^\circ\) and \(0<\theta<90\). The points \(D\) and \(C\) lie on \([OA]\) and \([OB]\) respectively, with \(OD=OC=r\text{ cm}\), and \(DC\) is an arc of a circle with centre \(O\). The region \(ABCD\) between the two arcs is decorated.

The sector \(OAB\) has area \(60\text{ cm}^2\) and perimeter \(34\text{ cm}\).

1. Find the value of \(\theta\).[5]

The decorated region \(ABCD\) has area \(45\text{ cm}^2\).

2. Hence find the value of \(r\).[2]