1965 IMO Problems/Problem 3

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Problem

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 $\varepsilon$ , parallel to lines $AB$ and $CD$ . The ratio of the distances of $\varepsilon$ from $AB$ and $CD$ is equal to $k$ . Compute the ratio of the volumes of the two solids obtained.

Solution

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1965 IMO Problems/Problem 3

From AoPSWiki

Problem

Solution