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Canadian Mathematical Olympiad - 2011 - Question 2

Source:

April 6, 2011
geometrycyclic quadrilateralangle bisectorgeometry proposed

Problem Statement

Let ABCDABCD be a cyclic quadrilateral with opposite sides not parallel. Let XX and YY be the intersections of AB,CDAB,CD and AD,BCAD,BC respectively. Let the angle bisector of ∠AXD\angle AXD intersect AD,BCAD,BC at E,FE,F respectively, and let the angle bisectors of ∠AYB\angle AYB intersect AB,CDAB,CD at G,HG,H respectively. Prove that EFGHEFGH is a parallelogram.
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