(i) The area of triangle AOB is \(\frac{1}{2} r^2 \sin \theta\).

The area of the sector AOB is \(\frac{1}{2} r^2 \theta\).

The area of the segment AXB is \(\frac{1}{2} r^2 \theta - \frac{1}{2} r^2 \sin \theta\).

Setting the areas equal: \(\frac{1}{2} r^2 \sin \theta = \frac{1}{2} r^2 \theta - \frac{1}{2} r^2 \sin \theta\).

Simplifying gives \(2 \sin \theta = \theta\), so \(p = 2\).

(ii) The chord length AB is \(2 \times 8 \sin \frac{2.4}{2} = 8 \sin 1.2 \times 2 \approx 14.9\).

The arc length AXB is \(2.4 \times 8 = 19.2\).

The perimeter of the segment AXB is the sum of these: \(14.9 + 19.2 = 34.1\).