This website contains problems from math contests. Problems and corresponding tags were obtained from the Art of Problem Solving website.

Tags were heavily modified to better represent problems.

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Found problems: 4

1953 Moscow Mathematical Olympiad, 240
Let $AB$ and $A_1B_1$ be two skew segments, $O$ and $O_1$ their respective midpoints. Prove that $OO_1$ is shorter than a half sum of $AA_1$ and $BB_1$.
skew midpoint geometric inequality geometry 3d geometry geometric inequalities solid geometry

1952 Moscow Mathematical Olympiad, 217
Given three skew lines. Prove that they are pair-wise perpendicular to their pair-wise perpendiculars.
skew perpendicular geometry 3d geometry solid geometry

1937 Moscow Mathematical Olympiad, 034
Two segments slide along two skew lines. On each straight line there is a segment. Consider the tetrahedron with vertices at the endpoints of the segments. Prove that the volume of the tetrahedron does not depend on the position of the segments
tetrahedron skew volume geometry 3d geometry solid geometry

1941 Moscow Mathematical Olympiad, 089
Given two skew perpendicular lines in space, find the set of the midpoints of all segments of given length with the endpoints on these lines.
skew geometry locus coordinate method