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BC bisector of <DBE wanted, AB=AC, AC = 2AD and AE = 2AC

Source: 2014 All-Ukrainian Correspondence MO of magazine ''In the World of Mathematics'', grades 5-12 p7

April 27, 2021
geometryisoscelesangle bisectorUkraine Correspondence

Problem Statement

Let ABCABC be an isosceles triangle (AB=ACAB = AC). The points DD and EE were marked on the ray ACAC so that AC=2ADAC = 2AD and AE=2ACAE = 2AC. Prove that BCBC is the bisector of the angle ∠DBE\angle DBE.
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