A Rotating Tetrahedron's Shadow

★ 7/10plane geometry Parametrization solid geometry Symmetry

Problem

A regular tetrahedron $ABCD$ has edge length $1$ . The plane $\alpha$ is parallel to edge $AB$ , and $E$ , $F$ are the midpoints of edges $AD$ and $BC$ . As the tetrahedron makes a full rotation about the axis $AB$ , find the range of the length of the projection $E_1F_1$ of segment $EF$ onto $\alpha$ .

Answer

Solution

Difficulty	7/10
Topics	plane geometry, Parametrization, solid geometry, Symmetry

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