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The non-empty set M and isometry Z

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January 11, 2011
geometry3D geometrytetrahedrongeometry proposed

Problem Statement

Let ABCDABCD be a regular tetrahedron and Z\mathbf{Z} an isometry mapping A,B,C,DA,B,C,D into B,C,D,AB,C,D,A, respectively. Find the set MM of all points XX of the face ABCABC whose distance from Z(X)\mathbf{Z}(X) is equal to a given number tt. Find necessary and sufficient conditions for the set MM to be nonempty.
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