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. The value of the area of \(\omega\) divided by \(\pi\) is in the form \(\frac{k}{m}\). Please find the value of \(k + m\).

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