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Math Help - Prove for a space geometry question

  1. #1
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    Unhappy Proof for a space geometry question

    Show that there exist one point equidistant from four non complainer distinct points (maybe it can be solved using axis of a circle )
    Last edited by lebanon; March 27th 2012 at 08:00 PM.
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  2. #2
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    Re: Proof for a space geometry question

    Quote Originally Posted by lebanon View Post
    Show that there exist one point equidistant from four non complainer distinct points (maybe it can be solved using axis of a circle )
    1. Four non-complanar points are located on a sphere. Thus you are looking for it's center.

    2. If the center of the sphere is C(c_1, c_2, c_3) then the equation of the sphere is:

    (x-c_1)^2+(y-c_2)^2+(z-c_3)^2=r^2

    Plug in the coordinates of the four points. You'll get a system of 4 equations which can be easily reduced to a system of 3 linear equations. Solve for (c_1, c_2, c_3).
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