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collinearity, circumcenter and circumircle related (Kharkiv City X 2016 - Ukr)

Source:

March 18, 2020
geometrycircumcirclecollinearCircumcenterKharkiv

Problem Statement

Let ADAD be the bisector of an acute-angled triangle ABCABC. The circle circumscribed around the triangle ABDABD intersects the straight line perpendicular to ADAD that passes through point BB, at point EE. Point OO is the center of the circumscribed circle of triangle ABCABC. Prove that the points A,O,EA, O, E lie on the same line.
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