Question 160
In the scalene triangle $ABC$, the bisector of angle $A$ meets side $BC$ at the point $D$. The lines passing through $D$ that are tangent to the circumcircles of triangles $ABD$ and $ACD$ meet the lines $AC$ and $AB$ at the points $E$ and $F$, respectively. If $BE$ and $CF$ meet at $G$, prove that the angles $\angle EDG$ and $\angle ADF$ are equal.