This is a very interesting problem. One thing I'd be interested in researching is the ratio between the 3 arcs in the scenario (https://en.m.wikipedia.org/wiki/

This is a very interesting problem. One thing I'd be interested in researching is the ratio between the 3 arcs in the scenario (https://en.m.wikipedia.org/wiki/File:Goat_problem_2D.svg https://en.m.wikipedia.org/wiki/File:Goat_problem_2D.svg), I'm sure this is a mathematical rabbit hole that would be exhausting to dive into.