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2019 Greece National Olympiad Q2

Source: 2019 Greece National Olympiad

March 11, 2019
geometry

Problem Statement

Let ABCABC be a triangle with AB<AC<BCAB<AC<BC.Let OO be the center of it's circumcircle and DD be the center of minor arc \overarc{AB}.Line ADAD intersects BCBC at EE and the circumcircle of BDEBDE intersects ABAB at ZZ ,(Z≠BZ\not=B).The circumcircle of ADZADZ intersects ACAC at HH ,(H≠AH\not=A),prove that BE=AHBE=AH.
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