Question 16
Let ABCD be a parallelogram. A variable line $l$ passing through the point $A$ intersects the rays $BC$ and $DC$ at points $X$ and $Y$, respectively. Let $K$ and $L$ be the centers of the excircles of triangles $ABX$ and $ADY$, touching the sides $BX$ and $DY$, respectively. Prove that the size of angle $KCL$ does not depend on the choice of the line $l$.