FI-MO 2013 Problem 3

The points $A,B,$ and $C$ lies on the circumference of the unit circle. Furthermore, it is known that $AB$ is a diameter of the circle and $$\frac{|AC|}{|CB|}=\frac{3}{4}.$$ The bisector of $ABC$ intersects the circumference at the point $D$ . Determine the length of the $AD$ .