JBMO 2001 Problem 2

Let $ABC$ be a triangle with $\angle C = 90^\circ$ and $CA \neq CB$ . Let $CH$ be an altitude and $CL$ be an interior angle bisector. Show that for $X \neq C$ on the line $CL$ , we have $\angle XAC \neq \angle XBC$ . Also show that for $Y \neq C$ on the line $CH$ we have $\angle YAC \neq \angle YBC$ .

Bulgaria