# 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:

\[x^2+(y-k)^2=r^2.\]

Find \(k+r\).