Question 22
Circle $C_1$ and $C_2$ each have radius $1,$ and the distance between their centers is $\frac{1}{2}.$ Circle $C_3$ is the largest circle internally tangent to both $C_1$ and $C_2.$ Circle $C_4$ is internally tangent to both $C_1$ and $C_2$ and externally tangent to $C_3.$ What is the radius of $C_4?$
