RU-ALLRUSSIAN 2021 Problem 101

On the side $BC$ of the parallelogram $ABCD$ , points $E$ and $F$ are given ( $E$ lies between $B$ and $F$ ) and the diagonals $AC, BD$ meet at $O$ . If it's known that $AE, DF$ are tangent to the circumcircle of $\triangle AOD$ , prove that they're tangent to the circumcircle of $\triangle EOF$ as well.