IMO Shortlist 2012 problem G7

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3. studenoga 2013.
Let ABCD be a convex quadrilateral with non-parallel sides BC and AD. Assume that there is a point E on the side BC such that the quadrilaterals ABED and AECD are circumscribed. Prove that there is a point F on the side AD such that the quadrilaterals ABCF and BCDF are circumscribed if and only if AB is parallel to CD.
Izvor: Međunarodna matematička olimpijada, shortlist 2012