Circle Center From Three Points

Geometry Level 4

The following three points lie on a circle in the \(xy\) plane. Coordinates are approximated to three decimal places.

\((x_1,y_1)\)\((8.590,9.213)\)
\((x_2,y_2)\)\((3.000,12.000)\)
\((x_3,y_3)\)\((-3.062,1.500)\)

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

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

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