IMO Shortlist 1965 problem 3
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Avg: 0,0 Given the tetrahedron
whose edges
and
have lengths
and
respectively. The distance between the skew lines
and
is
, and the angle between them is
. Tetrahedron
is divided into two solids by plane
, parallel to lines
and
. The ratio of the distances of
from
and
is equal to
. Compute the ratio of the volumes of the two solids obtained.
![ABCD](/media/m/9/c/e/9ce25711ba18d9663b73c3580de4bf5a.png)
![AB](/media/m/5/2/9/5298bd9e7bc202ac21c423e51da3758e.png)
![CD](/media/m/8/9/5/895081147290365ccae028796608097d.png)
![a](/media/m/6/d/2/6d2832265560bb67cf117009608524f6.png)
![b](/media/m/e/e/c/eec0d7323095a1f2101fc1a74d069df6.png)
![AB](/media/m/5/2/9/5298bd9e7bc202ac21c423e51da3758e.png)
![CD](/media/m/8/9/5/895081147290365ccae028796608097d.png)
![d](/media/m/f/7/d/f7d3dcc684965febe6006946a72e0cd3.png)
![\omega](/media/m/d/5/8/d58b95547061c22be95770ed7010f287.png)
![ABCD](/media/m/9/c/e/9ce25711ba18d9663b73c3580de4bf5a.png)
![\epsilon](/media/m/9/c/1/9c1cf4c5a8129e2d240ee3d8785936a4.png)
![AB](/media/m/5/2/9/5298bd9e7bc202ac21c423e51da3758e.png)
![CD](/media/m/8/9/5/895081147290365ccae028796608097d.png)
![\epsilon](/media/m/9/c/1/9c1cf4c5a8129e2d240ee3d8785936a4.png)
![AB](/media/m/5/2/9/5298bd9e7bc202ac21c423e51da3758e.png)
![CD](/media/m/8/9/5/895081147290365ccae028796608097d.png)
![k](/media/m/f/1/3/f135be660b73381aa6bec048f0f79afc.png)
Izvor: Međunarodna matematička olimpijada, shortlist 1965