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.

Posted by Brian Smith on 2004-07-17 18:59:46