ABCD is a trapezium with AB = CD, with vertices on the circle and with centre O. AD is a diameter of the circle. The radius of the circle is 4 units.

a. Find BC in term of theta.

b. Find the area of the trapezium in terms of theta and hence find the maximum area.

Image of the diagram for this question:

http://i45.tinypic.com/23s944h.png