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

alt text

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?

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up vote 7 down vote accepted

Congratulations! Looks to me like you have rediscovered Pappus' Hexagon Theorem.

The image from the link:

alt text

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That's it, thanks. Problem is that you can only google it if you know what it's called! – stevenvh Sep 3 '10 at 8:00
Looks like AC and DF don't even have to be parallel. – stevenvh Sep 3 '10 at 8:01
FYI, this works for 6 points on a conic section (Pascal's theorem). The case you have discovered is a degenerate case. – Soarer Sep 3 '10 at 8:49
@steven: I googled it! "collinear points theorems" and I got this page:… – Aryabhata Sep 3 '10 at 13:47
@moron: No I hadn't tried it first, but at least it looks like I'm pretty good at choosing a title for my question! :-) Thanks for the link. +1 – stevenvh Sep 3 '10 at 14:39

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