Sphere Center From Four Points

Geometry Level 5

The following four points lie on a sphere in the \(xyz\) coordinate system. Coordinates are approximated to three decimal places.

\((x_1,y_1,z_1)\)\((5.000,8.732,15.000)\)
\((x_2,y_2,z_2)\)\((2.000,7.000,17.000)\)
\((x_3,y_3,z_3)\)\((3.732,4.000,15.000)\)
\((x_4,y_4,z_4)\)\((0.653,10.702,13.695)\)

If the center of the sphere has coordinates \((h,k,m)\), determine \(h+k+m\).

Details and Assumptions:
Round \(h\), \(k\), and \(m\) individually to the nearest integer before adding them.

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