Hi bjhopper! Thanks again for your reply

I understand most of your explanation but I didn't understand some parts, where you said to swing arcs and a vertical line.

If you ever wish to make some quick graphs, not only on this thread. There's a tool called CaRMetal that is by java, so you don't have to install anything.

So we can better understand you. Search CaRMetal on Google, it is a French program

What do you mean with many triangles?

And what do you mean with fixing the length?

Here's what I got

and

If we were to equal those two equations, would we get anywhere?

About the Stewart's Theorem,

the theorem is

But we can't use it here with that few measures.

But I didn't want to do it with it,

The last time I did this question, I didn't get it right. That's why I am asking for it again.

I used a property of right triangles, and we don't know if this is a right triangle (eventually we do, but).

I don't know how you guys got AC=6 with the bisector theorem

If I get something wrong, it is maybe because it is late here and I am kind of tired hahaha

Thanks bjhopper!