Geometry – lines that intersect in the projective plane.

Consider three points $ A, B $ Y $ C $ in the projective plane not all in a line. Next, choose a point $ O $ and draw the lines that connect $ O $ with $ A, B $ Y $ C $ respectively. We will refer to these lines as the "blue lines". Then, we repeat this procedure with another point. $ O & # 39; $ on the plane; The corresponding lines will be called "red lines".

Then we define the points of intersection of the blue line through A and the red line through B, the blue line through B and the red line through C, the blue line through C and the red line through A, and we connect these points of intersection through lines with $ C, A $ Y $ B $ respectively. Prove that the last three lines are concurrent.


I would like to obtain a proof of the previous statement by constructing suitable cubic and / or conic (degenerate) and applying classical theorems.

Thank you