CONO-SUR 2011 Problem 5

Let $ABC$ be a triangle and $D$ a point in $AC$ . If $\angle{CBD} - \angle{ABD} = 60^{\circ}, \hat{BDC} = 30^{\circ}$ and also $AB \cdot BC = BD^{2}$ , determine the measure of all the angles of triangle $ABC$ .