(i) From the diagram, we have OQ = x + OC = 20. Using trigonometry in the right triangle, we have:

\(\sin 0.6 = \frac{x}{OC} \Rightarrow OC = \frac{x}{\sin 0.6}\)

Substitute into the equation: \(x + \frac{x}{\sin 0.6} = 20\)

Solve for \(x\): \(x = 7.218\)

(ii) The area of the sector is \(\frac{1}{2} \times 20^2 \times 1.2\).

The area of the circle with centre C is \(\pi \times 7.218^2\).

Total area outside the circle: \(\frac{1}{2} \times 20^2 \times 1.2 - \pi \times 7.218^2 = 76.3 \text{ cm}^2\)

(iii) Angle PCR is \(\pi - 1.2\).

Arc PR is \(7.218 \times (\pi - 1.2) = 14.01 \text{ cm}\).

Using trigonometry, \(OP = OR = \frac{x}{\tan 0.6}\).

Perimeter of OPSR: \(14.01 + 2 \times \frac{7.218}{\tan 0.6} = 35.1 \text{ cm}\)