# 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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