The second overlapping crescent moon solution the GPT provides is really interesting. If it was hard to find a counter example I wonder if there is a restricted

The second overlapping crescent moon solution the GPT provides is really interesting. If it was hard to find a counter example I wonder if there is a restricted case for the radius of the inner circles for which the proposed algorithm is true. I don't have the maths to determine this myself but would love to hear speculation from others.