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Pascal's mystic hexagram (Theorem)

If an hexagon $ADBFCE$ (not necessarily convex) is inscribed into a conic (in particular into a circle), then the points of intersections of opposite sides ($AD$ with $FC$, $DB$with $CE$ and $BF$ with $EA$) are collinear. This line is called the Pascal line of the hexagon.

A very special case happens when the conic degenerates into two lines, however the theorem still holds although this particular case is usually called Pappus theorem.

\includegraphics{hexpasc}



"Pascal's mystic hexagram" is owned by drini. [ owner history (1) ]
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See Also: Pappus's theorem

Other names:  Pascal line, Pascal's theorem

Attachments:
proof of Pascal's mystic hexagram (Proof) by mathcam
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Cross-references: Pappus theorem, line, collinear, opposite sides, intersections, points, circle, conic, inscribed, convex, hexagon
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This is version 6 of Pascal's mystic hexagram, born on 2002-01-08, modified 2005-01-19.
Object id is 1442, canonical name is PascalsMysticHexagram.
Accessed 9030 times total.

Classification:
AMS MSC51-00 (Geometry :: General reference works )

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