Circle $C_1$ and $C_2$ each have radius $1$, and the distance between their centers is $1/2$. Circle $C_3$ has its center at the midpoint of the line segment connecting the centers of $C_1$ and $C_2$, and its radius is $1/2$. Circle $C_4$ is internally tangent to both $C_1$ and $C_2$ and externally tangent to $C_3$. What is the radius of $C_4$?