I've got some thoughts on how to find the length of AB.
1. draw a circle and select three dots on in as A, B, and C;
2. DB=8cm, since the radius is 4cm, then DB=8=2x4 must be a diameter;
3. then triangle BAD is a right triangle with angle-BAD being 90 degree;
4. now in the right triangle BAD, you know lengths of two sides AD and BD, guess you could figure out how to find the length of the third side, i.e., AB.
*about the lengths of AC and BC, I find the provided constraints sort of insufficient; Is there any info that may be provided in the question statement?