2025 Nov TZ3 P2 Q5

Consider a circle and a sector.
The radius of the circle is \(8\) mm.
The radius of the sector is \(r\) mm and the acute angle at the centre is \(\theta\) radians.
This is shown in the following diagram.

The perimeter of the sector is \(1.5\) times the circumference of the circle.

1. Show that \(r = \frac{24\pi}{2 + \theta}\).

   [3]

It is given that the area of the circle is the same as the area of the sector.

2. Determine the value of \(\theta\).

   [3]