MathNet 2012 Question 50

Let $ABC$ be a triangle and let $\omega$ be a circle passing through $A,B$ and meeting the sides $[BC]$, $[AC]$ again at $D,E$, respectively. Let $K,L$ be the incentres of triangles $DAC$, $BEC$, respectively. Let $N$ be the intersection of the lines $EL$ and $DK$.

Prove that triangle $KNL$ is isosceles.