Question 43
Let $ABCD$ be an isosceles trapezium with bases $\overline{AB}$ and $\overline{CD}$. The diagonals of the trapezium meet at the point $S$, while $M$ denotes the midpoint of the leg $\overline{AD}$. The circle circumscribed to the triangle $BCM$ intersects $\overline{AD}$ again at the point $K$. Prove that the lines $SK$ and $AB$ are parallel.