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\includegraphics[max width=\textwidth, alt={}, center]{5e3e5418-7976-4232-8550-1da6420a3fcb-08_534_506_255_815} The diagram shows a motif formed by the major arc \(A B\) of a circle with radius \(r\) and centre \(O\), and the minor arc \(A O B\) of a circle, also with radius \(r\) but with centre \(C\). The point \(C\) lies on the circle with centre \(O\).

1. Given that angle \(A C B = k \pi\) radians, state the value of the fraction \(k\).
2. State the perimeter of the shaded motif in terms of \(\pi\) and \(r\).
3. Find the area of the shaded motif, giving your answer in terms of \(\pi , r\) and \(\sqrt { 3 }\).