Question 180
Let $K, L, M$ denote three points on the sides $BC, AB$ and $AC$ of $\triangle ABC$, so that $ALKM$ is a parallelogram. Points $S$ and $T$ are chosen on lines $KL$ and $KM$ respectively, so that the quadrilaterals $ASBK$ and $AKCT$ are both cyclic. Prove that $SLMT$ is cyclic if and only if $K$ is the midpoint of $BC$.