RU-SPB 2018 Problem 117

Points $A,B$ lies on the circle $S$ . Tangent lines to $S$ at $A$ and $B$ intersects at $C$ . $M$ -midpoint of $AB$ . Circle $S_1$ goes through $M,C$ and intersects $AB$ at $D$ and $S$ at $K$ and $L$ . Prove, that tangent lines to $S$ at $K$ and $L$ intersects at point on the segment $CD$ .