Backstory: I am currently making a program, that takes in position and radius of two circles, and outputs if they intersect at $0$, $1$, $2$, or $∞$ points. I have just found this edge case, and am not sure what to output for it.
Say, we have a circle with its center on $(0,0)$ and a radius of $3$, and the point circle, a circle with a radius of $0$, with it's center on $(0,3)$. The question is, how much intersection points do the two circles have?
In the name of God
Well, You can say a circle with radius 0, has only one point located on its perimeter, which is its center. To understand why this happens, notice circle's equation :
$r ^2 = (x-h)^2 + (y-k)^2$ where circle is (h,k).
If r = 0, the only solution to the equation is x = h and y = k . As a result, in this case, there is one point of intersection.