Question 60
Let $ABC$ be an isosceles triangle with $AB = AC$. On the extension of the side $[CA]$ we consider the point $D$ such that $AD \lt AC$. The perpendicular bisector of the segment $[BD]$ meets the internal and the external bisectors of the angle $\widehat{BAC}$ at the points $E$ and $Z$, respectively. Prove that the points $A, E, D, Z$ are concyclic.