I have a problem grasping how can I calculate following:
Given circle $A$ with radius $r_A$ and center point $S_A = (r_A, r_A)$ and circle B with radius $r_B$ and center point $S_B = (2r_A, d)$ calculate $d$ knowing that circles intersect in one point only and $d$ is smallest possible.
And I'm stuck with even starting it. Tried drawing it, but got to a point I just created following set of equations:
$\begin{cases} (x - r_A)^2 + (y - r_A)^2 \mbox{=} {r_A}^2 \\ (x - 2r_A)^2 + (y - d)^2={r_B}^2 \end{cases}$
This however gets me nowhere since I have 2 equations and 3 variables. What am I missing here?
The equation you are missing is the one of a line connecting points $(r_A,r_A)$ and $(2r_A,d)$. The intersection point $(x_P,y_P)$ is also on this line.
The easiest way to solve it, however, is by drawing it and realising that the intersection point $(x_P,y_P)$ is along this line and the distance between it and the point $(r_A,r_A)$ is $r_A$.