### Pascal's Hexagon Theorem

Pascal's
Theorem: if a hexagon is inscribed in a conic, then the three points at which
the pairs of opposite sides meet lie on a straight line.

Its dual is Brianchon's Theorem,
in which the sides (rather than the vertices) of the hexagon are incident to the
conic (*i.e.* the hexagon is circumscribed), and the intersections of major
diagonals (rather than the opposite sides) are concurrent.

Pascal's Theorem applies to a hexagon inscribed in any conic, and so it is a
generalization of Pappus' Theorem,
which considers only the case of a hexagon inscribed in a pair of lines.

. . . . . . a proof would be nice!

### Internet references

Cut-the-knot:
Pascal's Theorem gives a proof and a Java applet that lets you
explore it.

Cut-the-knot:
Pascal's Theorem, Homogeneous Coordinates

### Related pages in this website:

Summary of geometrical theorems

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