MathDB

Let

ABCDEFGH

be a cube of sidelength

a

and such that

AG

is one of the space diagonals. Consider paths on the surface of this cube. Then determine the set of points

P

on the surface for which the shortest path from

P

A

and from

P

G

have the same length

l.

Also determine all possible values of

l

depending on

a.

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