Before tackling this one, take a look at

this one.

+-------------D
/| /|
/ | / |
/ | / |
/ | / |
C-------------+ |
| | | |
| B--------|----+
| / | /
| / | /
| / | /
|/ |/
+-------------A

A, B, C and D are non-adjacent vertices of a cube. There is a point P in space such that PA=3, PB=5, PC=7, and PD=6. Find the distance from P to the other four vertices and find the length of the edge of the cube.

There are two answers, one with P outside the cube and one with P inside the cube.

(In reply to

rough stuff by rixar)

*"I have a very hard time picturing a point on the outside that shares the distance relationships with a point on the inside."*

I probably could have worded it better, but the two answers have cubes which are different sizes. The larger cube has point P on the inside and the smaller cube has point P on the outside.

I would recommend first finding the lengths from P to the other four vertecies before finding the sizes of the cubes.