I have an unusual problem. I've known this girl for a while now, she lives a few streets away from me, and her brother is an old classmate of mine. I used to see her around from time to time, she's even on my facebook, but we never really talked properly until a few weeks ago. On that ocassion I really felt that her and I got on well, exchanged good eye contact, and seemed to relate very well to each other. The problem is, I'm unlikely to see her again for a long time, if ever. Yes, she lives nearby, but we're extremely unlikely to be bump into eachother like that again, and her Brother and I aren't classmates anymore. We just don't run in the same circles.
But here's the thing, I'm not interested in her romantically; I actually would just love to be her friend, as she seems like a really nice, down to earth girl. But I don't know how? Could I sent her a message on Facebook? If so, what would I say? It would seem very odd and out of the blue since I never really spoke to her before, and I don't want to come across creepy, or give her the wrong idea. I genuinely just want to get to know her platonically.
However I fear she will think I want to date her by the mere fact that I am approaching her so randomly. How do you become friends with someone who has been an acquaintance for a long time, especially someone of the opposite sex? And what approach could I take in a facebook message?
Many thanks.