CZ-SK-MO 2020 Problem 5

Given an isosceles triangle $ABC$ with base $BC$ . Inside the side $BC$ is given a point $D$ . Let $E, F$ be respectively points on the sides $AB, AC$ that $|\angle BED | = |\angle DF C| > 90^o$ . Prove that the circles circumscribed around the triangles $ABF$ and $AEC$ intersect on the line $AD$ at a point different from point $A$ .

(Patrik Bak, Michal Rolínek)