Question 101
Outside a convex quadrilateral $ABCD$ we construct equilateral triangles $ABQ$, $BCR$, $CDS$ and $DAP$. Denoting by $x$ the sum of the diagonals of $ABCD$, and by $y$ the sum of line segments joining the midpoints of opposite sides of $PQRS$, we find the maximum value of $\frac{y}{x}$.