Let T1, T2, T3 be three triangles with the property: The Nine Point Circle centers N1, N2, N3 of T1, T2, T3, resp. are collinear.
I call the line N1N2N3 enneadic line of T1, T2, T3
See an example of an enneadic line in geometry of triangle Euclid 6930
Conjecture
Let A1A2A3... An be a regular n-gon, n>4.
There are three triangles of the n-gon having an enneadic line.
Problem
How many "different" enneadic lines are in a n-gon ?
(two enneadic lines are "different" if the 2 triads of the triangles are not symmetric)
Similarly we may ask for enneadic lines of 4 triangles.
PICTURES
Pentagon
Hexagon
Heptagon 1
Heptagon 2
Heptakaidecagon
Heptagon (4 triangles. Elias Hagos)
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