Given 3 circles:
- $C_1$ centered at $(0,0)$ with radius 1
- $C_2$ centered at $(a,0)$ with radius $a+1$
- $C_3$ centered at $(-a,0)$ with radius $a+1$
(so $C_1$ is internaly tangent to both $C_2$ and $C_3$ )
What are the centres of circle $C_4$ and $C_5$ that are tangent to all three circles?
I know they are on the $x=0$ axis but what is their $y$ coordinate?