Can I prove Brianchon's theorem using Ceva's? I am also wondering if parabola and hyperbola can be inscribed in a hexagon?
2026-03-28 14:18:24.1774707504
Can one prove Brianchon's theorem using Ceva's theorem?
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There is a proof in Hatton's Projective Geometry (lower right hand of pg 191).
One way to do this is study the proof of Pascal's Theorem using Menelaus' Theorem (e.g. here) and then dualize it. The final step uses a dual version of Carnot's theorem, which is discussed in the Hatton reference.
Also see Exercises 159-162 of Smith's Modern Geometry.