Four Dogs

Four dogs, A, B, C, and D are located at the vertices of a square. They start to run at the same time and at the same speed. A runs toward B, B runs toward C, C runs toward D, and D runs toward A.

Eventually they all meet in the center of the square. Why?

What are the paths followed by the four dogs?

What is the length of the path followed by each dog?

How many times does the path of each of the dogs cross a diagonal of the square? At what angle?

Suggestion
Implement the animation on a GSP sketch. Vary the speed of the animation to obtain different configurations. Here is one potential GSP sketch.