Let $k$ be the circumcircle of the acute triangle $ABC$. Its inscribed circle touches sides $BC$, $CA$ and $AB$ at points $D, E$ and $F$ respectively. The line $ED$ intersects $k$ at the points $M$ and $N$, so that $E$ lies between $M$ and $D$. Let $K$ and $L$ be the second intersection points of the lines $NF$ and $MF$ respectively with $k$. Let $AK \cap BL = Q$. Prove that the lines $AL$, $BK$ and $QF$ intersect at a point.
Problem
Source: IFYM - XI International Festival of Young Mathematicians Sozopol 2022, Theme for 11-12 grade,finals p2
Tags: geometry, incircle, concurrency, concurrent