The wording of your question is a bit confusing. By the distance from midpoint of to and , do you mean the distance and as I have in my diagram?
This is how I did the calculation, if this is wrong, just let me know.
As point, by letting and , we see that the triangles and are the same. Thus
Calculate for x with Pythagoras' theorem, and you'll find AC.
If my assumption is wrong, just let me know.