Pre svega, hvala na trudu, Nedeljko. Problem je originalno iz geometrije konika, a ja sam pokušao da ga prevedem u euklidsku geometriju, pa da ga tako rešim, što mi, nažalost, nije uspelo. Ne baratam analitičkim alatkama, koje ti koristiš, već me zanima sintetički pristup. Evo originala, pa ako ti možeš da pomogneš, hvala ti:
My original problem was:
Let c is a conic, ABCDEF is a Pascal hexagon(6 points on the conic c), sides of triangles ABC and DEF intersect pairwise in points IJKLMN.
I found using GeoGebra, that lines IJ, KL and MN are concurrent in point S (inside a conic). Is it Steiner point?
I found (6*5*4)/(3*2*1)=20 points, choosing pairs of triangles among 6 points.
Number of Steiner points is also 20, but ABCDEF, ACDFEB, ACBEDF is not a configuration in article about Steiner points, so i cant prove this beautiful...
Theorem:Let ABC and DEF be two triangles lie on a conic and points IJKLMN are pairwise intersections of it's sides.
Then opposite vertices of this hexagon are concurrent.
Vice cersa is also true.
Do you know something about that?