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It isnt normal no, but it can happen
What is your height? And how much are you eating on average per day?
When you're a teenager, having an irregular period is completely normal. When you lose weight your cycle can get messed up, too. Anorexic girls often miss their periods (I'm not saying you're anorexic, it just has to do with weight loss).
If you're worried about it, I suggest that you talk to your doctor about it.
If it has been a year since your last got your period, I highly suggest that you go talk to your doctor about it.
You lost ten pounds in a month?! Dear, how much are you eating? (Or how little?) Ten pounds in one months seems like a lot. Do you count your calories? How many calories do you eat in a day? If you don't, it's fine. Try listing down how much you eat per day/ and how much exercise you do.
It could be that your body doesn't have enough calories..