- The length of the dotted line dc is known

The circle is probably not necessary.

In my head ab and cd are perpendicular (??).

The angle inside point c (ie the angle opposite ab within the triangle abc) is known. I'll call this theta just for a moment.

In the triangle bcd the angle inside c (ie the angle opposite db) is half theta.

I keep drawing lots of pretty pictures but haven't actually got anywhere with the problem! I could probably work it out if ab was parallel to the y axis (2d space) but I cannot guarantee that it will be so there's my problem!

Any thoughts on the above?

Thanks in advance,

Kazatan