In a circle of radius 12cm, radii OA, OB and OC are drawn so that ∠AOB=120∘ and ∠AOC=60∘, with all three points A,B,C on the same side of OA. The region bounded by arc AB, arc AC and chord BC is shaded.
a. (i) Find the area of the segment corresponding to arc AB.
b. (ii) Find the area of the segment corresponding to arc AC.
c. (iii) Determine the area of the shaded region between the two arcs.