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concyclic points wanted, related to circumcircle, midpoint, perpendicular

Source: Greece JBMO TST 2019 p1

April 29, 2019
geometryConcycliccircumcircleperpendicular

Problem Statement

Consider an acute triangle ABCABC with AB>ACAB>AC inscribed in a circle of center OO. From the midpoint DD of side BCBC we draw line (ℓ)(\ell) perpendicular to side ABAB that intersects it at point EE. If line AOAO intersects line (ℓ)(\ell) at point ZZ, prove that points A,Z,D,CA,Z,D,C are concyclic.
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