Question 91
Let $ABC$ be a triangle with $A \lt 90^{\circ}$. Outside of the triangle we consider isosceles triangles $ABE$ and $ACZ$ with bases $AB$ and $AC$, respectively. If the midpoint $D$ of the side $BC$ is such that $DE \perp DZ$ and $EZ = 2 \cdot ED$, prove that $\widehat{AEB} = 2 \cdot \widehat{AZC}$.
