Thread: Problem with two triangles

Hi all,
I'm an engineering student with little remaining knowledge about simple Euclideian geometry (and big shame too). I need to solve a problem about which I'm clueless. I don't even know if there's a solution, so I'm asking you for help.

Two triangles ABT and ABO have an edge in common (AB). I know all angles and edges of the first one, and also that AT=BT. In the second one, I know just the AOB angle and, naturally, the common edge. There's also a segment, OT, joining the opposite vertices and intersecting AB in X. I know both the angles AOX and BOX.

I need to calculate any of these edges: AX, BX, OA or BA - or any of these angles: ATX, BTX, OAB or OBA. You'll agree that knowing one of them allows me to know all of the others.

I'm attaching a drawing of the whole thing.

Many many thanks for all the help!!

Greetings
Enrico