Consider two circles on a plane given by equations :
$(x-x_{c1})^2 + (y-y_{c1})^2 = r_1^2 $
$(x-x_{c2})^2 + (y-y_{c2})^2 = r_2^2$
I need to find a pair of points $(x_1,y_1)$ on Circle 1 and $(x_2,y_2)$ on Circle two which are distance $K$ apart
By Euclidean Distance, I get
$K^2 = (x_1-x_2)^2 +[(y_{c1}-y_{c2}) + \sqrt{r_1^2 - (x_1-x_{c1})^2} - \sqrt{r_2^2 - (x_2-x_{c2})^2} ]^2 $
There are two unknowns : $x_1$ and $x_2$. I need to find one pair of such rational $x_1$ and $x_2$,