(a) The angle \(ACB\) is given as \(k\pi\) radians. From the mark scheme, \(k = \frac{2}{3}\).

(b) The perimeter of the shaded motif is the circumference of the circle with radius \(r\), which is \(2\pi r\).

(c) To find the area of the shaded motif:

- The area of the major sector \(OAB\) is \(\frac{1}{2} r^2 \times \frac{4\pi}{3} = \frac{2\pi r^2}{3}\).

- The area of the minor sector \(CAOB\) is \(\frac{1}{2} r^2 \times \frac{\pi}{3} = \frac{\pi r^2}{6}\).

- The area of triangle \(ACB\) is \(\frac{1}{2} r^2 \sin \frac{\pi}{3} = \frac{r^2 \sqrt{3}}{4}\).

- The area of the shaded motif is the area of the major sector minus the area of the minor sector and the triangle: \(\frac{2\pi r^2}{3} - \left( \frac{\pi r^2}{6} + \frac{r^2 \sqrt{3}}{4} \right) = \frac{\pi r^2}{3} + \frac{r^2 \sqrt{3}}{2}\).