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In the Extended Euclidean Plane, let l and m be two lines that intersect at the point ). Let A, B, C be three points on l other than o and let A', B', C' be three points on m other than o. Assume that the line AA', BB', and CC' are concurrent at a point P. Let E= AB'(intersect)A'B, F=AC'(intersect)A'C. Then the points O,E,F are collinear.

Here's what I wrote, but idk if it's correct.

In the Extended Euclidean Plane, let L and M be two points lying on the line O. Let a,b,c be three lines containing L other than line O and let a'b'c' be three lines containing M other than line O. Assume that the points A and A' are collinear, B and B' are collinear, and C and C' are collinear and the lines AA', BB', and CC' all contain P. Let line e contains the points A',B,A,B' and line f contain the points A,C',A',C. Then, the lines o,e, and f are concurrent.

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  • $\begingroup$ When you say "assume that the points $A$ and $A'$ are collinear," it seems that these points have not been defined yet in the dual statement. $\endgroup$ – hunter Mar 27 at 15:34
  • $\begingroup$ @hunter I see. What exactly are these points though? That's where I'm not understanding how my dual statement works. $\endgroup$ – lj_growl Mar 27 at 15:42
  • $\begingroup$ The dual to the line $AA'$ will be the intersection of the duals of $A$ and $A'$. $\endgroup$ – hunter Mar 27 at 16:00

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