Circumcircle Of A Triangle In A Coordinate Plane

Geometry Level 3

Let A(8,4)A(-8, 4) and B(6,6) B(6, 6) be points in the coordinate plane. Point C(0,k) C(0, k) is such that the circumcircle of ABC \triangle ABC has equation x2+y2+2x10y24=0 x^2+y^2+2x-10y-24=0 . Determine the sum of all possible values of k k .

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