Given two circles $A$ and $B$ with distance from their radius $d$ , is it possible to calculate the radius of the circles? If yes, how?
What if we add a $3^{rd}$ circle $C$ , with distance $d_2$ from center of $B$ and $C$ and given that $C$ is half of $A$ i.e $ r_a = 2r_c$ , is it mathematically possible? 
Best Answer
In the first example, the only restriction you have is $r_A + r_B = d$. There are infinitely many possibilities for the two radii so you cannot determine them
In the second example, notice that $d = r_A + r_B = 2r_C + r_B$. Therefore, $d - d_2 = r_C$.
Now, that you know $r_C$, you can compute $r_A = 2r_c$ and $r_B = d_2 - r_C$.