KöMaL 2017 B4891

The circles $S_1$, $S_2$, $S_3$ pairwise touch each other on the outside. Let $A$, $B$ and $C$ denote the common points of the circles $S_1$ and $S_2$, $S_1$ and $S_3$, $S_2$ and $S_3$, respectively. Line $AB$ intersects the circles $S_2$ and $S_3$ again at points $D$ and $E$, respectively. Line $DC$ intersects circle $S_3$ again at $F$. Prove that triangle $DEF$ is right-angled.