IGO 2016 E4

In a right-angled triangle $ABC$ ( $\angle A = 90^o$ ), the perpendicular bisector of $BC$ intersects the line $AC$ in $K$ and the perpendicular bisector of $BK$ intersects the line $AB$ in $L$ . If the line $CL$ be the internal bisector of angle $C$ , find all possible values for angles $B$ and $C$ .

by Mahdi Etesami Fard