RU-SPB 2021 Problem 95

Given is an isosceles trapezoid $ABCD$ , such that $AD$ and $BC$ are bases and $AD=2AB$ , and it is inscribed in a circle $c$ . Points $E$ and $F$ are selected on a circle $c$ so that $AC$ || $DE$ and $BD$ || $AF$ . The line $BE$ intersects lines $AC$ and $AF$ at points $X$ and $Y$ , respectively. Prove that the circumcircles of triangles $BCX$ and $EFY$ are tangent to each other.