Sam Lloyd Puzzles ... (3)

It is told that 3 neighbors who shared a small park, as shown in the sketch, had a falling out. The owners of the large house, complaining that his neighbor's chickens annoyed him, built an enclosed pathway from his door to the gate at the bottom of the picture.

Then the man on the right built a path to the gate on the left, and the man on the left built a path to the gate on the right.

None of the paths crossed. Can you draw the lines correctly?