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Parallel line in cyclic kite

Source: Sharygin Finals 2017, Problem 8.1

August 4, 2017
geometryProjective

Problem Statement

Let ABCDABCD be a cyclic quadrilateral with AB=BCAB=BC and AD=CDAD = CD. A point MM lies on the minor arc CDCD of its circumcircle. The lines BMBM and CDCD meet at point PP, the lines AMAM and BDBD meet at point QQ. Prove that PQ∥ACPQ \parallel AC.
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