How to approach a shy girl?

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So there's a girl I have already approached once before, however she blushed and quickly ended the conversation and walked off. I could tell it was simply because she didn't expect to be approached out of the blue - even though we had made eye contact before then.

I keep wanting to go up to her again but I expect the same thing to happen. My question is, how do I approach her eg. what do I say to make her feel comfortable?

I first approached her on campus and asked if she was from my hometown because she looked familiar. This was a lie but I don't think it was unacceptable, however she obviously said no and walked off in a rush.

I want to approach her again but I need a good situation/opening line that won't make her shy.
How to approach a shy girl?
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