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 , all angles of which are measured as a integer number of degrees. It turned out that the bases of these triangles are equals and for each of them on the ray there is a point such that , and the angle 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?