Team Selection Test for EGMO 2019

Let $ABC$ be a triangle satisfying $|AB|=|AC|$. Let $D$ be a point on smaller arc $AC$ of circumcircle $\omega$ of $ABC$. Let $E$ be the symmetric point of $B$ with respect to the line $AD$. The line $BE$ intersects $\omega$ at $F$. The tangent line of $\omega$ at $F$ intersects the line $AC$ at $K$ and the lines $DF$ and $AB$ intersect at $L$. Show that the points $K,L,E$ are collinear.