Prove for a space geometry question

• March 27th 2012, 07:45 PM
lebanon
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 )
• March 27th 2012, 10:09 PM
earboth
Re: Proof for a space geometry question
Quote:

Originally Posted by lebanon
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 $(c_1, c_2, c_3)$.