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DE//AB wanted, isosceles ABC, BE=CD NZMO 2021 R1 p5

Source:

September 20, 2021
parallelogramisoscelesgeometry

Problem Statement

Let ABCABC be an isosceles triangle with AB=ACAB = AC. Point DD lies on side ACAC such that BDBD is the angle bisector of ∠ABC\angle ABC. Point EE lies on side BCBC between BB and CC such that BE=CDBE = CD. Prove that DEDE is parallel to ABAB.
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