<human>: Can you give me a shortened version of the text?

Okay, to begin, I know this sounds weird, which is why I'm asking and not just doing.

You know how Facebook has that feed of "people you may know" on the side bar? One time I saw this *beautiful* girl on there, she really caught my eye. I clicked, because well, what is a beautiful girl doing on my "you may know" list? Turns out she is a friend of one of my friends that I don't really talk to. That friend is a girl in a committed relationship that actually resembles a couple of 60 year olds (they turned really boring when they started dating. If I'm invited over, I may go, maybe not. Point is, a bit of a disconnect with the mutual friend)

I asked her about her once told her how I saw her and thought it was weird and asked if she thought it was. She said yes (she's also a bit of a prude so I'm not sure I should take that as solid evidence) and kind of laughed about it, saying the girl came over once and really just trailed onto something else. I told her she should invite her to her next get together (I said I planned on making the next one anyway because I felt bad missing so many) This never really happened.

So my question is: Although I'd hate to use Facebook as a first meeting, would it be weird if I messaged her saying how I had seen her and that I couldn't help but try to reach out? I am much, much better at not appearing creepy in person than I am on the internet. Granted... that's mostly thanks to the internet itself. If you think I should, how would you word it/how would you *not* word it.
<bot>: saw a mutual friend on Facebook. Wanted to say hi as mutual friend is no help in the matter. The internet makes me think too much.