KMO 2018 Problem 1

Let there be an acute triangle $\triangle ABC$ with incenter $I$ . $E$ is the foot of the perpendicular from $I$ to $AC$ . The line which passes through $A$ and is perpendicular to $BI$ hits line $CI$ at $K$ . The line which passes through $A$ and is perpendicular to $CI$ hits the line which passes through $C$ and is perpendicular to $BI$ at $L$ . Prove that $E, K, L$ are colinear.