You may have some compatible astrology going on with Geminis, like your rising sign, your moon sign, your venus sign. Also, Gemini and Cancer are next door neighbors in Western Astrology, which makes for a kind of capatibility. I have also found that often men will be very compatible with women who are similar to their Mother’s astrology. Ie, if your mother was a gemini, or the equivaliency in Chinese astrology of gemini (horse), you may find gemini women very wonderful to be around.
My husband’s mother is a Horse in Chinese astrology, and I’m a Gemini, and I actually think that has helped our relationship a lot, because he is used to that Gemini energy in a close relationship.
Sounds like you are doing fine getting along with the gemini women in your life. I know that for me, being respected, and knowing that I have my freedom (in thought, action, feeling) is very important to me. I need to be trusted and respected, that makes me feel safe and appreciated. If I am not treated with respect, I am “outta there”.
Good luck with your love life.
And, on a side note, only make a move on that lady at work if you are really serious, since she is engaged. Don’t want to mess with her emotions unless you are REALLY serious.