The incircle of a triangle $ABC$ has center $I$ and touches $AB , BC , CA$ at $C_1 , A_1 , B_1$ respectively. Let $BI$ intersects $AC$ at $L$ and let $B_1I$ intersects $A_1C_1$ at K. Show that $KL$ is parallel to $BB_1$.
I’ve draw some lines and try to find angles but it didn’t work. Can anyone give me some hints (or solution) please. Thank you very much!
(I didn’t try trigonometry or complex bash yet because it would be very ugly.)