The circle is just a visualization of a concept, not a proof. The Quora answer clearly refers to this concept: https://mathworld.wolfram.com/ProjectivelyExtendedRealNumbers.html

The page clearly states this is a non-standard number system. You cannot use it in the general case. It is a common practice for mathematicians to come up with new number systems with new rules and see where it leads to. Maybe there’s a practical use for it?

This is the same case here. Some mathematician came up with a new number system where 1/0 is treated as a new number with special properties and see what it leads to. Any new conclusion made in this number system is probably not applicable in any standard number system.

The article also mentions this number system: https://mathworld.wolfram.com/AffinelyExtendedRealNumbers.html

Similarly this is a number system that has been constructed such that infinity exists as a number, but in this case negative infinity is a distinct number. 1/0 is not defined under this system as a result. This is a non-standard system as well, so shouldn’t be used unless it’s clearly intended.