32- Gacia Capitan's line-9 points are collinear

Today I recheck a problems of me at here: ADPGEP#624 , I generalization following:

Let  be a triangle, a line  on the plane,  meets three sides  respectively at . Let  is any point on the plane. meets  respectively at . Define  cyclically.

 meets  at , define  cyclically.

Let  be a points on the line , such that ; define cyclically.

I named the line through  is Gacia Capitan's line

Please see also: Garcia Capitan blog

Now we have  also lie on Gacia Capitan's line.

- Further more: Two triangle  and  are perpective, perpector is P(please see the figure attachment).  meets  at ,  meets  at ,  meets  at . Then  are collinear (Desargues's theorem).  also lie on this line. 

Now we have 9 points are collinear