I'm working on this problem (not homework):
Let $ABC$ be a triangle and $D$ a point on the side $AC$. If C\hat{B}D-A\hat{B}D = 60°, B\hat{D}C = 30° and $AB \cdot BC =BD^2$, find the angles of the triangle $ABC$.
I've been working on it for a while, and have managed to express all the angles in terms of a single variable, but I have no idea how to use the relationship between the sides. I've tried to construct right triangles to use trigonometry or Pythagoras' Theorem, but it just ends up introducing new sides I don't care about. I drew a picture to make things clearer for me, but sadly I don't have a scanner or a camera right now, so I can't upload it.
It would be great if you could give me a few tips instead of the full answer; I'd like to figure it out (mostly) on my own.