In \(\triangle{ABC}\) with side lengths \(AB = 13\), \(AC = 12\), and \(BC = 5\), let \(O\) and \(I\) denote the circumcenter and incenter, respectively. A circle with center \(M\) is tangent to the legs \(AC\) and \(BC\) and to the circumcircle of \(\triangle{ABC}\). Find the area of \(\triangle{MOI}\). The answer is in the form \(\frac{k}{m}\), where \(\frac{k}{m}\) is in simplest form. Please find the value of \(k + m\).

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