# 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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