The distance between the centers of the three circles which are mutually tangent to each other externally are 10, 12, and 14 units. Find the area of the smallest circle.

Small, Medium, Large = the circles
$\begin{matrix}
S & + & M & \, & \, & = & 10 & \, & \leftarrow \, \text{Equation (1)} \\
S & \, & \, & + & L & = & 12 & \, & \leftarrow \, \text{Equation (2)} \\
\, & \, & M & + & L & = & 14 & \, & \leftarrow \, \text{Equation (3)}
\end{matrix}$
 

 

From Equations (1), (2), and (3)
$S = 4$
 

Area of the small circle
$\text{Area} = \pi (4^2) = 16\pi ~ \text{unit}^2$