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Length of paths on a cube.

Source: Germany 2013 - Problem 4

December 5, 2022
geometry3D geometrycubelengthpaths

Problem Statement

Let ABCDEFGHABCDEFGH be a cube of sidelength aa and such that AGAG is one of the space diagonals. Consider paths on the surface of this cube. Then determine the set of points PP on the surface for which the shortest path from PP to AA and from PP to GG have the same length l.l. Also determine all possible values of ll depending on a.a.
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