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.