Deductive geometry - Similarity and congruence

Finally, the last geometry problem I am stuck with. Please help me get this one too!

http://i301.photobucket.com/albums/n.../Noether11.png

Thanks so much to anyone who helps, I am certain this involves similarity and congruence.

We have .

But .

Then .

Use Pitagora's theorem: .

Replace BC with and AB with 10 and find AC.