CMO 2020 Problem 2

In triangle $ABC$ , $AB>AC.$ The bisector of $\angle BAC$ meets $BC$ at $D.$ $P$ is on line $DA,$ such that $A$ lies between $P$ and $D$ . $PQ$ is tangent to $\odot(ABD)$ at $Q.$ $PR$ is tangent to $\odot(ACD)$ at $R.$ $CQ$ meets $BR$ at $K.$ The line parallel to $BC$ and passing through $K$ meets $QD,AD,RD$ at $E,L,F,$ respectively. Prove that $EL=KF.$