UA-UMO 1997 Problem 93

The incircle of a triangle $ABC$ is tangent to its sides $AB,BC,CA$ at $M,N,K,$ respectively. A line $l$ through the midpoint $D$ of $AC$ is parallel to $MN$ and intersects the lines $BC$ and $BD$ at $T$ and $S$ , respectively. Prove that $TC=KD=AS.$