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Similarity appearing from nowhere

Source: All-Russian 2021/9.4

April 19, 2021
geometry

Problem Statement

Given an acute triangle ABCABC, point DD is chosen on the side ABAB and a point EE is chosen on the extension of BCBC beyond CC. It became known that the line through EE parallel to ABAB is tangent to the circumcircle of △ADC\triangle ADC. Prove that one of the tangents from EE to the circumcircle of △BCD\triangle BCD cuts the angle ∠ABE\angle ABE in such a way that a triangle similar to △ABC\triangle ABC is formed.
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