PAMO 2019 Problem 4

The tangents to the circumcircle of $\triangle ABC$ at $B$ and $C$ meet at $D$ . The circumcircle of $\triangle BCD$ meets sides $AC$ and $AB$ again at $E$ and $F$ respectively. Let $O$ be the circumcentre of $\triangle ABC$ . Show that $AO$ is perpendicular to $EF$ .