Question 72
Let $\triangle ABC$ be an isosceles triangle with $AB = AC$. Point $D$ is chosen on the smaller arc $AB$ of the circumcircle of $ABC$. Point $E$ is chosen on the ray $AD$ outside the segment $AD$ so that points $A$ and $E$ lie on the same side of line $BC$. The circumcircle of triangle $BDE$ intersects side $AB$ at point $F \neq B$. Prove that the lines $EF$ and $BC$ are parallel. (R. Zhenodarov)