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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 $H$?

rj7k8
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  • If we change H from a hexagon to two triangles, there must be a conic tangent to each of the six lines. I'm looking forward an easy way to prove it: https://math.stackexchange.com/questions/4271783 – auntyellow Oct 09 '21 at 09:10

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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.

timon92
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