Very beautiful and hard problem

[ins-]

It is given the convex quadrilateral ABCD. Let:
P is intersection point of the diagonals AC and BD,
M is intersection point of the lines AB and CD,
N is intersection point of the lines AD and CB.
The line PN intersects AB and CD at the points X and Z respectively.
The line PM intersects BC and AD at the points Y and T respectively.
Prove that the lines MN, XY, ZT and AC intersects at a common point.

My questions are the following:
I know the statement is true but i don't know how to prove it, can you prove the problem?
Is it a famous theorem?
Have you ever seen the problem proposed?

[Хорхе]

Don't know if it's familiar, but via projective transformations one can write zillions of such problems.

And it is not hard at all. Send $ABCD$ to a square with a projective transformation and you will arrive to a trivial statement.

[ins-]

More opinions?

-- Сб апр 17, 2010 17:18:21 --

http://xahlee.org/projective_geometry/q ... teral.html what I found using google.

[ins-]

Now we have 4 solutions to this problem. You can see more solutions at:
http://www.mathlinks.ro/viewtopic.php?p=1849480#1849480