A problem I (re)invented

[ins-]

Inside the triangle ABC is chosen a point P.
The line AP intersects BC at A1.
The line BP intesrects CA at B1.
The line CP intesrects AB at C1.
The line through B1 parallel to CC1intersects the segments AP and AB at the points K and L respectively.
The line through A1 parallel to CC1 intersects the segments BP and AB at the points M and N respectively.
Prove that CC1, KN and LM intersects at a common point.

[VoloCh]

Is it "Olympiad" problem?
Let start with that: http://en.wikipedia.org/wiki/Ceva's_theorem

[ins-]

I know Ceva's theorem but I'm wondering how it can be used in such a way to help us.

I'm so stupid ... the problem is very easy ... it can be solved without Ceva ... there is a 3 row solution.
I'm interested to see a solution using Ceva. I started with composing the problem with the idea to create a problem that uses Ceva's theorem. Often I first create problem statements without knowing the solution and then I'm starting with searching the solution. I'm sorry if I bother you.

[Хорхе]

Again the problem will become straightforward if you send the line $CC_1$ to infinity with a projective transformation.

In fact, there is a rule which allows to simplify (or even to trivialize) a lot of problems: use a projective transformation whenever you have a problem about intersections of lines and/or collinearity of points.

[ins-]

Tnank you very much. My problem have at least 4-5 solutions. It is almost trivial but there is something interesting in it.