concyclic and equal circles wanted, 3 squares related
Source: 2020 XXIII All-Ukrainian Tournament of Young Mathematicians named after M. Y. Yadrenko, Qualifying p12
May 4, 2021
geometrySquaresConcyclicequal circlesUkrainian TYM
Problem Statement
On the side of the square , the point is chosen and the equal squares and are constructed ( and lie inside the square). Let be the midpoint of , is the incenter of the triangle . Prove that:
a) the points lie on the same circle;
b) the circles inscribed in triangles and have the same radii.