$\frac{[\text { Similar triangles (other) })]}{[\underline{\text { Trapezoids (other) }}]}$

In trapezoid $A B C D$, side $A B$ is perpendicular to the bases $A D$ and $B C$. Point $E$ is the midpoint of side $C D$.

Find the ratio $A D: B C$, if $A E=2 A B$ and $A E \perp C D$.