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Brianchon's
Theorem: in a hexagon circumscribed about a conic, the major diagonals, i. e.
the diagonals joining vertices with the opposite ones, are concurrent.
Its dual is Pascal's Theorem,
in which the vertices (rather than the sides) of the hexagon are incident to the
conic (i.e. the hexagon is inscribed), and the intersections of opposite
sides (rather than the major diagonals) are collinear.
. . . . . . proof?
Cut-the-knot: Brianchon's Theorem gives a proof and a Java applet that lets you explore it.
The webmaster and author of this Math Help site is Graeme McRae.