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perpendicularity wanted, isosceles triangle and parallelogram related

Source: 2002 Argentina OMA L3 p5

June 15, 2020
geometryparallelogramisoscelesperpendicular

Problem Statement

Let △ABC\vartriangle ABC be an isosceles triangle with AC=BCAC = BC. Points D,E,FD, E, F are considered on BC,CA,ABBC, CA, AB, respectively, such that AF>BFAF> BF and that the quadrilateral CEFDCEFD is a parallelogram. The perpendicular line to BCBC drawn by BB intersects the perpendicular bisector of ABAB at GG. Prove that DE⊥FGDE \perp FG.
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