I am writing a game and need to figure out some math. If I have a circle with the equation $r^2 = (x-d)^2+(y-e)^2$, where $r$, $d$, and $e$ are constants, and a point $A(a,b)$, how do I find the point(s) on the circumference of the circle that are a given straight-line distance $D$ from $A$?
I'm in high school, so I don't have the most extensive math knowledge. However, my first attempt was to find the $x$-values by isolating the $y$-value in the circle equation and substituting it into the distance formula. Then, I would simply substitute the $x$-values back into the circle equation to get the corresponding $y$-values. However, I can't isolate $y$.
In the end, I will only use this where $A$ is on the circumference of the circle already.