Four Distances Problem
by luimichael, Nov 1, 2007, 12:59 AM
Given a cube with base ABCD and top EFGH such that E is vertically above A.
Point P is inside the cube with PA = a, PB = b and PD = d and PE = e.
Determine the length of AB in terms of a, b, d and e.
Solution:
Point P is inside the cube with PA = a, PB = b and PD = d and PE = e.
Determine the length of AB in terms of a, b, d and e.
Solution:
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.![$ 3u^4 + 2(a^2 - b^2 - d^2 - e^2)u^2 \newline + [(a^2 - b^2)^2 + (a^2 - d^2)^2 + (a^2 - e^2)^2] = 0$](http://latex.artofproblemsolving.com/c/e/7/ce76ee40a46226a4bae0d0c9814639fc791801cf.png)
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