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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

1 Answers 1

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

The image from the link:

alt text

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    @Stevenh: if you google "theorem three points collinear" the 2nd match is the Wikipedia page on Desargues theorem, which mentions Pappus's theorem in the 2nd paragraph. So it's really not that hard to find.2010-09-03