# 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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