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Parallelogram in cyclic quadrilateral

Source: European Mathematical Cup 2014, Senior Division, P3

December 14, 2014
geometryparallelogramcircumcirclecyclic quadrilateralgeometry unsolved

Problem Statement

Let ABCDABCD be a cyclic quadrilateral in which internal angle bisectors ∠ABC\angle ABC and ∠ADC\angle ADC intersect on diagonal ACAC. Let MM be the midpoint of ACAC. Line parallel to BCBC which passes through DD cuts BMBM at EE and circle ABCDABCD in FF (F≠DF \neq D ). Prove that BCEFBCEF is parallelogram
Proposed by Steve Dinh
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