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angle <ABC wanted if ABC,ACD,BCD are all isosceles with D between A,B

Source: 2015 Portugal p2

October 10, 2020
geometryisoscelesangles

Problem Statement

Let [ABC][ABC] be a triangle and DD a point between AA and BB. If the triangles [ABC],[ACD][ABC], [ACD] and [BCD][BCD] are all isosceles, what are the possible values of ∠ABC\angle ABC?
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