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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?
TIA
Steven

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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
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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
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@steven: I googled it! "collinear points theorems" and I got this page: gogeometry.com/geometry/… –  Aryabhata Sep 3 '10 at 13:47
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@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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