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APMO 2017: (ADZ) passes through M

Source: APMO 2017, problem 2

May 14, 2017
geometryAPMO

Problem Statement

Let ABCABC be a triangle with AB<ACAB < AC. Let DD be the intersection point of the internal bisector of angle BACBAC and the circumcircle of ABCABC. Let ZZ be the intersection point of the perpendicular bisector of ACAC with the external bisector of angle ∠BAC\angle{BAC}. Prove that the midpoint of the segment ABAB lies on the circumcircle of triangle ADZADZ.
Olimpiada de Matemáticas, Nicaragua
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