IMO 1965 Problem 3

Given the tetrahedron $ABCD$ whose edges $AB$ and $CD$ have lengths $a$ and $b$ respectively. The distance between the skew lines $AB$ and $CD$ is $d$ , and the angle between them is $\omega$ . Tetrahedron $ABCD$ is divided into two solids by plane $\epsilon$ , parallel to lines $AB$ and $CD$ . The ratio of the distances of $\epsilon$ from $AB$ and $CD$ is equal to $k$ . Compute the ratio of the volumes of the two solids obtained.