Vanishing Point

Geometry Level 4

Two circles are in the interior of \(\angle A\), and are tangent both to each other and to both sides of \(\angle A\). If their radii are in the ratio \(17:25\), then \(\cos \angle A = \frac{m}{n}\), where \(m\) and \(n\) are positive coprime integers. Find \(m+n\).

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