Elementary Geometry for College Students (6th Edition)

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