Circles with radii 2 and 6 have centers at points $O_{1}$ and $O_{2}$, respectively, and touch each other externally at point $C$. A common external tangent and a common internal tangent are drawn to the circles. These tangents intersect at point $D$. Find the radius of the circle inscribed in triangle $O_{1} O_{2} D$.

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Prove that $D B$ is the altitude of the right triangle $O_{1} D O_{2}$, drawn from the vertex of the right angle $D$.

## Answer

$2(\sqrt{3}-1)$.