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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