Brianchon's Theorem

Theorem

Let tangents to $6$ points on a conic section $K$ form a hexagon $H$ to circumscribe the $K$.

Then the main diagonals of $H$ meet at a single point.



Proof


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Also see


Source of Name

This entry was named for Charles Julien Brianchon.


Sources

  • 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $6$
  • 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): Brianchon's theorem
  • 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $6$
  • 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): Brianchon's theorem
  • 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): Pascal's theorem
  • 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): Brianchon's theorem
  • 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): Pascal's theorem
  • 2021: Richard Earl and James Nicholson: The Concise Oxford Dictionary of Mathematics (6th ed.) ... (previous) ... (next): Brianchon's theorem
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