# Circle the Drain

Geometry Level 5

A triangle has sides 10,17 and altitude 8 through the vetex common to both sides. Find the area of another triangle formed when the centers of following circles are joined (as shown in the figure above):

If the answer can be written as $$a + \dfrac{m}{n}$$, where $$a,m$$ and $$n$$ are positive integers, $$m<n$$ and $$m$$ and $$n$$ are coprime. Find $$a+m+n$$.

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