Question 51
Let $ABCD$ be a cyclic quadrilateral, with $AB \lt CD$, whose diagonals intersect at the point $F$ and $AD$, $BC$ intersect at the point $E$. Let also $K$, $L$ be the projections of $F$ onto the sides $AD$, $BC$ respectively, and $M$, $S$, $T$ be the midpoints of $EF$, $CF$, $DF$. Prove that the second intersection point of the circumcircles of the triangles $MKT$, $MLS$ lies on the side $CD$.