Find angles in triangle ABC where AB = AC and AD = DB = BC

[Natasha1]

In a triangle ABC, AB = AC and AD = DB = BC. Find the size of the angle BAD? Find the angles of triangle ABC?

Just need a few hints to get this problem started please?

 

[quantumdude]

Natasha: HallsofIvy responded here with most of the solution. I've soft deleted it and will restore it once you have shown some work on this problem.
He used analytic geometry and he started as follows:

Set up a coordinate system so that the origin is at point B (B is at (0,0))and the positive x-axis is in the direction of C. Call the length of side BC "c" so that C is at (c,0).

You will need to find coordinates of other points and then find equations of the lines that contain the sides of the triangles. Give that a shot and post what you come up with.