Brianchon's Theorem states that for any hexagon circumscribed about a conic section, meaning each of its six sides is tangent to the conic, the three main diagonals connecting opposite vertices all meet at a single point. Named for Charles Julien Brianchon, it is the projective dual of Pascal's Theorem, exchanging the roles of points and lines.
Facts
StatementWhen a hexagon is circumscribed around a conic section, its principal diagonals meet in a single point. 1 Classification
Statement FormCharacterization Theorem 1 Connections
Has Statement Form
In Branch
Source Brianchon's theorem, Wikipedia
Principal Result Of
Source Charles Julien Brianchon (Wikipedia)
Proved By
Source Brianchon's theorem, Wikipedia
Sources
1. Brianchon's theorem, Wikipedia
Lead paragraph
when a hexagon is circumscribed around a conic section, its principal diagonals (those connecting opposite vertices) meet in a single point.
Proved By: Charles Julien Brianchon, Lead sentence
It is named after Charles Julien Brianchon (1783-1864).
In Branch: Geometry, Lead sentence
In geometry, Brianchon's theorem is a theorem stating that when a hexagon is circumscribed around a conic section, its principal d
View the SourceCharles Julien Brianchon (Wikipedia)
Principal Result Of: Charles Julien Brianchon, WorkQuote, Principal Result Of: Charles Julien Brianchon, Work
Brianchon is best known for his proof of Brianchon's theorem (1810).
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