Question 94
A family $L$ of $2006$ lines on the plane is given in such a way that it doesn't contain parallel lines and it doesn't contain three concurrent lines. We say that the line $l_1 \in L$ is *bounding* the line $l_2 \in L$, if all intersection points of the line $l_2$ with other lines from $L$ lie on the one side of the line $l_1$. Prove that in the family $L$ there are two lines $l$ and $l'$ such that the following two conditions are hold simultaneously:
1) the line $l$ is bounding the line $l'$;
2) the line $l'$ is not bounding the line $l$.
1) the line $l$ is bounding the line $l'$;
2) the line $l'$ is not bounding the line $l$.