KöMaL 2017 B4858

Points $A$ and $B$ are separated by a unit distance. The unit circles $k_A$ and $k_B$ centred at $A$ and $B$ intersect at points $C$ and $D$, respectively. Let $k_C$ denote the circle centred at $C$ and passing through $D$. $F$ is that intersection of line $AC$ and circle $k_C$ which is farther away from $A$. $G$ is the other intersection of circle $k_A$ and line $DF$. Show that $\angle GAD=90^\circ$.