MathDB

9

Part of 1977 IMO Longlists

Problems(1)

The non-empty set M and isometry Z

Source:

1/11/2011
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.
geometry3D geometrytetrahedrongeometry proposed