TH-TMO 2020 Problem 6

Let the incircle of an acute triangle $\triangle ABC$ touches $BC,CA$ , and $AB$ at points $D,E$ , and $F$ , respectively. Place point $K$ on the side $AB$ so that $DF$ bisects $\angle ADK$ , and place point $L$ on the side $AB$ so that $EF$ bisects $\angle BEL$ . [list=a] []Prove that $\triangle ALE\sim\triangle AEB$ . []Prove that $FK=FL$ . [/list]