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FA // BC if AB=AC, DB _|_BC, CE=2BC, FC //AB

Source: VII - Mathematics Regional Olympiad of Mexico Northeast 2007 P2

September 17, 2022
geometryparallelisosceles

Problem Statement

In the isosceles triangle ABCABC, with AB=ACAB=AC, DD is a point on the extension of CACA such that DBDB is perpendicular to BCBC, EE is a point on the extension of BCBC such that CE=2BCCE=2BC, and FF is a point on EDED such that FCFC is parallel to ABAB. Prove that FAFA is parallel to BCBC.
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