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Circle inscribed in the quadriteral

Source: Problem 2, Polish NO 1993

October 6, 2005
inequalitiesgeometrytrapezoidparallelogramgeometric transformationhomothetygeometry solved

Problem Statement

A circle center OO is inscribed in the quadrilateral ABCDABCD. ABAB is parallel to and longer than CDCD and has midpoint MM. The line OMOM meets CDCD at FF. CDCD touches the circle at EE. Show that DE=CFDE = CF iff AB=2CDAB = 2CD.
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