CR-MO 2017 G2

Consider the right triangle $\vartriangle ABC$ right at $A$ and let $D$ be a point on the hypotenuse $BC$ . Consider the line that passes through the incenters of $\vartriangle ABD$ and $\vartriangle ACD$ , and let $K$ and $L$ the intersections of said line with $AB$ and $AC$ respectively. Show that if $AK = AL$ then $D$ is the foot of the altitude on the hypotenuse.