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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