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IMO Shortlist 2012, Geometry 7

Source: IMO Shortlist 2012, Geometry 7

July 29, 2013
geometryhomothetyincenterIMO Shortlist

Problem Statement

Let ABCDABCD be a convex quadrilateral with non-parallel sides BCBC and ADAD. Assume that there is a point EE on the side BCBC such that the quadrilaterals ABEDABED and AECDAECD are circumscribed. Prove that there is a point FF on the side ADAD such that the quadrilaterals ABCFABCF and BCDFBCDF are circumscribed if and only if ABAB is parallel to CDCD.
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