Question 158
A circle intersects sides $BC$, $CA$, $AB$ of $ABC$ at two points for each side in the following order: \{$D_1, D_2$\}, \{$E_1, E_2$\} and \{$F_1, F_2$\}. Line segments $D_1E_1$ and $D_2E_2$ intersect at point $L$, $E_1F_1$ and $E_2D_2$ intersect at point $M$, $F_1D_1$ and $F_2E_2$ intersect at point $N$. Prove that $AL$, $BM$ and $CN$ are concurrent. (posed by Ye Zhonghao)