MathDB
Geometry with many parallels and perpendiculars

Source: Francophone 2024, Junior P3

April 4, 2024
geometrygeometry proposed

Problem Statement

Let ABCABC be an acute triangle with AB<ACAB<AC and let OO be its circumcenter. Let DD be a point on the segment ACAC such that AB=ADAB=AD. Let EE be the intersection of the line ABAB with the perpendicular line to AOAO through DD. Let FF be the intersection of the perpendicular line to OCOC through CC with the line parallel to ACAC and passing through EE. Finally, let the lines CECE and DFDF intersect in GG. Show that AGAG and BFBF are parallel.
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