Connect the curve

Calculus Level 3

The figure shows the graph of \(f\left( x \right) =x+\frac { 1 }{ x } \)

The circle is tangent to the graph in 1st and 3rd quadrant and is the smallest of its kind.

The area of the circle is in the form \[A\pi \left( B+\sqrt { C } \right) \] where \(A,B,C\) are integers with \(C\) square free.

Find \(A+B+C\).

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