Three isosceles triangles

Take the isosceles triangle ABC with AC = AB.
      Point D on side CB is such that
the triangles CDA and DBA are isosceles
with CD = AD, and DB = AB.
      1. Find the angles of the triangle ABC.
      2. Prove that the area of the triangle DBA equals
          the geometric mean of the areas of the triangles
          CDA and ABC:   = .
      3. Prove that point D divides the side CB
          in the golden  ratio.     
      

Answers:
1. The angles ACD and ABD equal 36 deg, the angle BAC equals 108 deg.
2. : : = .
3. CD : DB = DB : CB.