you're correct about everything except them not sharing a root. look back further. or do i have to do it for you..

https://en.m.wiktionary.org/wiki/%CE%B4%CE%B1%CE%AF%CE%BC%CF%89%CE%BD#Ancient_Greek

https://en.m.wiktionary.org/wiki/%CE%B4%E1%BF%86%CE%BC%CE%BF%CF%82#Ancient_Greek

i hate that people don't know this. shouldn't be surprising at all.

you're correct about everything except them not sharing a root. look back further. or do i have to do it for you..

https://en.m.wiktionary.org/wiki/%CE%B4%CE%B1%CE%AF%CE%BC%CF%89%CE%BD#Ancient_Greek

https://en.m.wiktionary.org/wiki/%CE%B4%E1%BF%86%CE%BC%CE%BF%CF%82#Ancient_Greek