Twins in the Trigon

Geometry Level 5

The figure above shows two equal circles of radius \(r\) that are inscribed inside a triangle with side lengths 3, 4, 5.

The two circles share 1 tangent point.

If \(r\) can be expressed as \( \frac AB\), where \(A\) and \(B\) are coprime positive integers, find \(A+B\).

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