# Collinear points theorem

I was droodling a bit and a given moment I drew the following construction:

It appears that the three blue intersections are collinear (red line), no matter how I draw the construction lines. If this is always true, I assume that this a know fact [otherwise I have my first theorem! :-) erm conjecture, since I can't prove it :-( ].
What's the theorem called?
TIA
Steven

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