Let $H$ be a hexagon formed by six points lying on a conic in the plane.
Is there a conic tangent to each of the six lines comprising $H$?
2026-03-27 19:33:45.1774640025
Is there a conic tangent to each of the six lines comprising a conic-inscribed hexagon?
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In general, no. The necessary and sufficient condition for this to hold is that the main diagonals of hexagon are concurrent. This is called Brianchon's theorem.