IMO PROBLEM 1965

[MATHPRITOM]

A tetrahedron ABCD is given. The lengths of the edges AB and
CD are a and b, respectively, the distance between the lines AB and CD
is d, and the angle between them is equal to ω. The tetrahedron is divided
into two parts by the plane π parallel to the lines AB and CD. Calculate
the ratio of the volumes of the parts if the ratio between the distances of
the plane π from AB and CD is equal to k.