I got 3 GSDs--they are good deterrants for raccoons, oppossuns, skunks, etc. I would never put them up against coyotes. Right now it's mating season and food is scarce. They are meaner and hungry. As big as my dogs are they are supervised when outside. I try to go ecerything possible to make sure all animals are protected.
Coyotes are good for sending one in, dog chases and the rest of the pack are waiting to make the kill. A large dog is a meal for them.
GSD? German Shepard dogs? If they can’t take out a coyote then I don’t know what kind of breeding you’re getting, but it’s very poor! My uncle keeps two German shepherds outside full time in Dawson Creek Northern B.C. Canada For Grizzlies and Cougars. -20 to -30 Celsius during winter.
They have taken down one cougar and run off several bears, they are pretty much completely untrained just very territorial. They will be 2 this year (both females, littermates that would have been culled due to non-desirable color in their coats)
I think it’s more likely there’s a wolf problem you’re looking at, not coyotes! With the size of the print from the OP I wouldn’t discount a cross breed or possibly a wolf, they are actually smaller than most people think!