Question 26
Let $ABCD$ be a parallelogram. A variable line $l$ through the point $A$ intersects the rays $BC$ and $DC$ at $X$ and $Y$ respectively. Let $K$ and $L$ be the centres 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 $l$. (Short-list, IMO-2005)