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isosceles wanted, parallelogram ABCD, BC=GC , AB=AH

Source: 2013 Portugal MO p1

October 9, 2020
geometryparallelogram

Problem Statement

Consider a parallelogram [ABCD][ABCD] such that ∠DAB\angle DAB is an acute angle. Let GG be a point in line ABAB different from BB such that BC‾=GC‾\overline{BC}=\overline{GC}, and let HH be a point in line BCBC different from BB such that AB‾=AH‾\overline{AB}=\overline{AH}. Prove that triangle [GDH][GDH] is isosceles.
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