Answer
The length of the radius of the small circle is 4
Work Step by Step
In $\triangle ABC$, the angle $\angle B = 90^{\circ}$
In $\triangle OTC$, the angle $\angle T = 90^{\circ}$
The angle $\angle C$ is part of both triangles.
Therefore, $\triangle ABC \cong \triangle OTC$
We can find the length of $OT$:
$\frac{OT}{OC} = \frac{AB}{AC}$
$\frac{OT}{OC} = \frac{AB}{(2)(OC)}$
$OT = \frac{AB}{2}$
$OT = \frac{8}{2}$
$OT = 4$
The length of the radius of the small circle is 4
