The answer to the question in the title, that then it will not easily fall down into the manhole (just try with ellipsoidal or square covers ...), is a property of circles I never learnt in school. Yet it seems important! So the question: Is there some good reference, book, webpages, papers, others,... for such important but forgotten properties of simple geometrical figures? Geometry in mechanics (practical, simple, traditional mechanics, not the quantum variant ...), geometry in architecture, geometry in other applied and practical areas. There must be something out there, but I cannot find it by googling ...
A similar question here, but different, was Real-world examples of more "obscure" geometric figures