OME 2019 Problem 6

In the scalene triangle $ABC$ , the bisector of angle A cuts side $BC$ at point $D$ . The tangent lines to the circumscribed circunferences of triangles $ABD$ and $ACD$ on point D, cut lines $AC$ and $AB$ on points $E$ and $F$ respectively. Let $G$ be the intersection point of lines $BE$ and $CF$ . Prove that angles $EDG$ and $ADF$ are equal.