MathNet 2009-part-02 — 175 problems (EN–VI) Question 42

Let $ABC$ be a triangle in which $AB \gt AC$; $AM$ be the median and $AK$ be the angle bisector with $M, K$ on $BC$. Let $L$ be a point on $AM$ such that $KL$ is parallel to $AC$. Prove that $CL$ is perpendicular to $AK$.