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\includegraphics[max width=\textwidth, alt={}, center]{11bfe5bd-604c-43e5-81e7-4c1f5676bcbb-4_611_668_1699_737}
The diagram shows a sector of a circle with centre \(O\) and radius 20 cm . A circle with centre \(C\) and radius \(x \mathrm {~cm}\) lies within the sector and touches it at \(P , Q\) and \(R\). Angle \(P O R = 1.2\) radians.
- Show that \(x = 7.218\), correct to 3 decimal places.
- Find the total area of the three parts of the sector lying outside the circle with centre \(C\).
- Find the perimeter of the region \(O P S R\) bounded by the \(\operatorname { arc } P S R\) and the lines \(O P\) and \(O R\).