RU-ALLRUSSIAN 1974 Problem 10

In the triangle ABC, angle C is 90 deg and $\mathrm{AC} = \mathrm{BC}$ . Take points D on CA and E on CB such that $\mathrm{CD} = \mathrm{CE}$ . Let the perpendiculars from D and C to AE meet AB at K and L respectively. Show that $\mathrm{KL} = \mathrm{LB}$ .