BY-MO 1995 Problem 4

Given a triangle $ABC$ , let $K$ be the midpoint of $AB$ and $L$ be the point on the side $AC$ such that $AL = LC + CB$ . Show that if $\angle KLB = 90^o$ then $AC = 3 CB$ and conversely, if $AC = 3 CB$ then $\angle KLB = 90^o$ .