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Three pairwise skew lines in space

Source: Vietnam NMO 1988 Problem 6

February 2, 2009
geometrygeometric transformationreflectiongeometry unsolved

Problem Statement

Let a a, b b, c c be three pairwise skew lines in space. Prove that they have a common perpendicular if and only if Sa∘Sb∘Sc S_a \circ S_b \circ S_c is a reflection in a line, where Sx S_x denotes the reflection in line x x.
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