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DA bisector of <EDF if <AEF = <FDB, <AFE = <EDC, equilateral ABC

Source: 2015 All-Ukrainian Correspondence MO of magazine ''In the World of Mathematics'', grades 5-12 p8

April 27, 2021
geometryequal anglesangle bisectorEquilateralUkraine Correspondence

Problem Statement

On the sides BC,ACBC, AC and ABAB of the equilateral triangle ABCABC mark the points D,ED, E and FF so that ∠AEF=∠FDB\angle AEF = \angle FDB and ∠AFE=∠EDC\angle AFE = \angle EDC. Prove that DADA is the bisector of the angle EDFEDF.
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