I am looking for proof of a problem as follows:
Let three points $A, B, C$ are collinear. Let three lines $a, a_1, a_2 $ through $A$, three lines $b, b_1, b_2 $ through $B$ three lines $c, c_1,c_2$ through $C$. Such that $a_1 \parallel b_2; b_1 \parallel c_2, c_1 \parallel a_2 $. Let $A_1=a \cap b_1, A_2=a\cap c_2$ $B_1=b\cap c_1, B_2=b \cap a_2$, $C_1=c \cap a_1, C_2=c \cap b_2$. Then show that midpoints of $A_1C_2, B_1A_2, C_1B_2$ are collinear.
The problem on configuration of the Pappus theorem