In the diagram in the left below, AD is a diameter of the circle and is tangent to line m at D. If AD=1 AND BC is perpendicular to m, show that:

a) AB + BC = 1 +cos(x) - cos^2(x)

b) What value of x makes the sum AB + BC a maximum?

http://img168.imageshack.us/img168/6434/abcdcp3.jpg