Bài thi học sinh giỏi toán Áo quốc 2004
Problem 3 of the Austrian Mathematical Olympiad 2004
We are given a convex quadrilateral ABCD with ∠ADC = ∠BCD > 90°.
Let E be the intersection of the line AC with the line parallel to AD through B and F be the intersection of the line BD with the line parallel to BC through A. Show that EF is parallel to CD.