Question: Goat and wolf - a persecution problem

The following problem is old and quite challenging. I found it in a publication from 1959. I have the source and my own solution. I was able to solve it quite laboriously a few years ago using MC14 – but not recently with Maple. Therefore, I'm interested in instructive Maple solutions, just as previous puzzle solutions here have helped me further in using this software. I thank you for that.

A wolf observes a goat. It is grazing in a meadow, tied to a rope. Naturally, he wants to catch the goat and considers whether his starting position is favorable. He estimates that he and the goat will be moving at the same speed at the beginning of the hunt and throughout the pursuit, and that the goat will constantly hold the rope taut to maintain its distance for escape reasons. Now, as he approaches the goat at a constant top speed, the same speed as the goat is fleeing in a circular arc, he asks himself: Where do I need to start from to guarantee success? Are there starting positions that rule out a successful hunt? What happens if I manage to sneak into the grazed area first?