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35th Austrian Mathematical Olympiad 2004

Source: round1, problem3

February 11, 2009
geometry unsolvedgeometry

Problem Statement

Given is a convex quadrilateral ABCD ABCD with \angle ADC\equal{}\angle BCD>90^{\circ}. Let E E be the point of intersection of the line AC AC with the parallel line to AD AD through B B and F F be the point of intersection of the line BD BD with the parallel line to BC BC through A A. Show that EF EF is parallel to CD CD
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