Triangle and a semicircle

Geometry Level 4

In the triangle shown above, \(AB=12\), \(BC=18\) and \(AC=25\). A semicircle is drawn so that its center lies on \(AC\) and so that it is tangent to \(AB\) and \(BC\). If \(O\) is the center of the semicircle, find the area of the region inside the triangle but outside the semicircle. If your answer is of the form \(\dfrac{a\sqrt{6479}-6479\pi}{b}\), where \(a\) and \(b\) are positive integers, give your answer as \(a+b\).

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