In the figure, circular arcs $AC$ and $BC$ have centers at $B$ and $A$, respectively. A smaller circle is tangent to both $\stackrel{⌢}{\mathrm{AC}}$ and $\stackrel{⌢}{\mathrm{BC}}$, and to the segment $\overline{AB}$. If the length of segment $\overline{AB}$ is $8$, what is the area of the smaller tangent circle?