Points \(A(6,13)\) and \(B(12,11)\) lie on circle \(\omega\) in the plane. Suppose that the tangent lines to \(\omega\) at \(A\) and \(B\) intersect at a point on the \(x\)-axis. Find the value of \(\frac{\text{Area of }\omega}{\pi}\) in the format \(\frac{k}{m}\), and give the sum of k and m.

Let's think step by step and output the final answer within \boxed{}.
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