Show that there exist one point equidistant from four non complainer distinct points (maybe it can be solved using axis of a circle )

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- Mar 27th 2012, 07:45 PMlebanonProof 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 )

- Mar 27th 2012, 10:09 PMearbothRe: Proof for a space geometry question
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 $\displaystyle C(c_1, c_2, c_3)$ then the equation of the sphere is:

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

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 $\displaystyle (c_1, c_2, c_3)$.