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 Skip Navigation LinksMath Help > Geometry > Polygons and Triangles > Cyclic Quadrilateral > Brianchon's Hexagon Theorem

Brianchon's Hexagon Theorem

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?

Internet references

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

Related pages in this website:

Summary of geometrical theorems

 

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