KGYSAK - ~지오? vs. ~지요? vs. ~죠?

Another reason my teacher is awesome is that she'll answer just about any question I have regardless of how trivial or basic it may seem. Today's puzzle was as follows:

I see "~하지오" a lot. I have always been confused by ~하지오 and ~하지요. I know that ~하죠 is just a shortened form but what is the original, correct spelling? Form the horse's mouth:

"잘 지내지오?" - 이것은 spelling 맞춤법이 틀렸어요
"잘 지내지요?" - 이것이 맞아요.
"잘 지내죠?" - 이것은 "지요?"의 shortened word (줄임말)이에요. 지요 = 죠

There you have it. Just like 께 and 게 it's a simple spelling error that doesn't really ruffle up any feathers. Thus ends another tasty Korean Grammar You Should Already Know.