The diagram shows a circle with centre O and radius 8 cm. Points A and B lie on the circle. The tangents at A and B meet at the point T, and AT = BT = 15 cm.

(i) Show that angle AOB is 2.16 radians, correct to 3 significant figures.

(ii) Find the perimeter of the shaded region.

(iii) Find the area of the shaded region.