KöMaL 2005 K63

In the triangle ABC , $X$ is the midpoint of side $AB$ and $Y$ is the midpoint of side $AC$. $BY$ and $CX$ intersect at $S$. Show that $a$) the areas of the triangles SBX and SCY are equal; $b$) the areas of triangle SBC and quadrilateral AXSY are equal.