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.

Answer

Let

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.