# 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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