Need to know: Length of segment AB

Known information:

Each circle has a radius of 10cm. The centers all lie on line OE. Line OD intersects the middle circle and is tangent to the last circle.

I'm in trig, but I don't know if that's this problem. We haven't learned chords, secants or tangent lines but I know general info.

What I have figured out:

I drew a line done from the tangent point, I'm assuming that the angle off OE is the right triangle. The line down from point D is 10cm. Line OE is 50cm to the middle of the last circle. Angle O is arctan (10/50). I have no idea how any of this helps me though.

Thanks for sticking with it this far! :-)