The diagram shows sector OAB with centre O and radius 11 cm. Angle AOB = \(\alpha\) radians. Points C and D lie on OA and OB respectively. Arc CD has centre O and radius 5 cm.

(i) The area of the shaded region ABDC is equal to \(k\) times the area of the unshaded region OCD. Find \(k\).

(ii) The perimeter of the shaded region ABDC is equal to twice the perimeter of the unshaded region OCD. Find the exact value of \(\alpha\).