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2019 IGO Elementary P4

Source: 6th Iranian Geometry Olympiad (Elementary) P4

September 20, 2019
IGOIrangeometry

Problem Statement

Quadrilateral ABCDABCD is given such that ∠DAC=∠CAB=60∘,\angle DAC = \angle CAB = 60^\circ, and AB=BD−AC.AB = BD - AC. Lines ABAB and CDCD intersect each other at point EE. Prove that ∠ADB=2∠BEC. \angle ADB = 2\angle BEC.
Proposed by Iman Maghsoudi
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