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3 isosceles triangles, same base, angles of integer degrees, BE=AC

Source: 2019 XXII All-Ukrainian Tournament of Young Mathematicians named after M. Y. Yadrenko, Qualifying p8

May 5, 2021
geometryisoscelesIntegersUkrainian TYM

Problem Statement

Hannusya, Petrus and Mykolka drew independently one isosceles triangle ABCABC, all angles of which are measured as a integer number of degrees. It turned out that the bases ACAC of these triangles are equals and for each of them on the ray BCBC there is a point EE such that BE=ACBE=AC, and the angle AECAEC is also measured by an integer number of degrees. Is it in necessary that: a) all three drawn triangles are equal to each other? b) among them there are at least two equal triangles?