Your problem sounds like a pursuit curve.

Have you looked here:

]]>The questions:

1. Will the dog be able to catch the rabbit before it reaches the safe refuge?

2. What would be the shape of its path and it's precise mathematical formula?

3. Is there a better path the smarter dog would have chosen?

Only by actually drawing the path in small segments I have tried to solve the problem.I would appreciate if someone could do the appropriate math.

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