TITLE: Collinear points theorem
QUESTION [5 upvotes]: 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

REPLY [9 votes]: Congratulations! Looks to me like you have rediscovered Pappus' Hexagon Theorem.
The image from the link: