Orthogonal Circles

Geometry Level 4

\[\large{\begin{eqnarray} (x-153)^2+y^2&=&185^2 \\ (x+153)^2+y^2&=&185^2 \\ x^2+(y-1380)^2&=&196^2 \\ \end{eqnarray} }\]

Above shows the equations for 3 circles.

Two circles are orthogonal to each other if where they intersect meets at right angles. The circle that is orthogonal to all three of the circles above can be written as:


Find \(k+r\).


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