RU-ALLRUSSIAN 2021 Problem 94

Given an acute triangle $ABC$ , point $D$ is chosen on the side $AB$ and a point $E$ is chosen on the extension of $BC$ beyond $C$ . It became known that the line through $E$ parallel to $AB$ is tangent to the circumcircle of $\triangle ADC$ . Prove that one of the tangents from $E$ to the circumcircle of $\triangle BCD$ cuts the angle $\angle ABE$ in such a way that a triangle similar to $\triangle ABC$ is formed.