AB= 1/2CD, therefore, AD=CD=2AB.

In the right angle △ABD, CD=2AB, so BD=√3AB.

BC=BD+CD=√3AB+2AB=8, AB=8(2-√3).

CD=2AB=2×8(2-√3)= 16(2-√3)

Answer: The length of the CD is 16(2-√3).