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IA references question!!

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Hello everyone!! 

For my math IA, I decided to do some things related to the hanging chain problem. Long story short, there is a part where I need to create a general equation for a circle, given that it goes through 3 points A, B and C- whose coordinates are variable. I managed to do this without consulting any source whatsoever. I wrote everything in my own words, using my own method, and I'm seriously not sure where to find this exact method online/in a book somewhere. 

However, I still am 99% sure that someone, somewhere, somewhen has derived a general equation for a circle- given 3 points (that have variable coordinates). But as I said, I personally didn't use any such source. 

My question is, is it okay if I don't cite anything there, and present this as my own idea (which it was)? Since it was my idea to actually derive this formula, regardless whether someone somewhere has done it before, the IB won't have the "right" to accuse me of plagiarism. That's my opinion. But I'm not willing to take any risks here. Should I look for a source and fakely cite it, and pretend that I got my ideas from there?

I'm considering to do something like this, in order to avoid getting accused of plagiarism, without actually being guilty of it. 

Any feedback is welcome! 

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I think solving this is something reasonable enough that an HL student could do it without referencing anything. So it's completely fine. It would be different if you mentioned anything beyond HL then indeed you do need to cite those. So i presume if you use HL or below math in this derivation, it's fine, but if you looked up some formula then you need to cite that. 

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