Radius of a sector from a perimeter condition, then its angle from equal areas with a circle

A circle has radius \(5\) cm. A sector of another circle has radius \(r\) cm and an acute angle of \(\theta\) radians at its centre, as shown in the diagram below.

The perimeter of the sector is \(1.2\) times the circumference of the circle.

1. Show that \(r=\frac{12\pi}{2+\theta}\).[3]

The area of the sector is also equal to the area of the circle.

2. Find the value of \(\theta\).[3]