Putnam 1989 B5

Label the vertices of a trapezoid $T$ (quadrilateral with two parallel sides) inscribed in the unit circle as $A, B, C, D$ so that $AB$ is parallel to $CD$ and $A, B, C, D$ are in counterclockwise order. Let $s_1, s_2$, and $d$ denote the lengths of the line segments $AB, CD$, and $OE$, where E is the point of intersection of the diagonals of $T$, and $O$ is the center of the circle. Determine the least upper bound of $\frac{s_1-s_2}{d}$ over all such $T$ for which $d\ne 0$, and describe all cases, if any, in which it is attained.