Four Tangent Circles

Geometry Level 5

\(4\) circles meet at \(6\) points, sharing common tangent lines through each point.

The flat areas of the circles are

\(165\pi \)
\(220\pi \)
\(297\pi \)
\(540\pi \)

A sphere passes through all \(4\) circles, so that the circles are on the surface of the sphere. The surface area of the sphere is

\(A\pi \)

Find integer \(A\)


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