So let's say that I have a standard $(x, y)$ coordinates system, the center of a circle $(0,1)$ and the radius $(1)$. How can I determine that whether the point $(0,0)$ touches the circumference or not?
I don't need to determine if the point is inside or outside the circumference but my problem is related with its touching the circumference of the following circle.
The general equation for the circle is $(x-c_x)^2 + (y-c_y)^2 = r^2$, where $(c_x,c_y)$ is the center and $r$ is the radius. A point $(x,y)$ lies on the circle (the disk's boundary) if it satisfies the above equation. If instead: $(x-c_x)^2 + (y-c_y)^2 < r^2$ then it is inside the disk, and similarly it is outside for $>$.
Edit: This can be extended to arbitrary high dimensions, let $\vec{c}\in \mathbb{R}^n$ be the center of the $n$ dimensional hypersphere, and $r$ be its radius. Then a point $\vec{v}\in \mathbb{R}^n$ lies on its surface if $|\vec{v}-\vec{c}|^2 = r^2$, where $|\vec{a}| = \sqrt{\sum_{i=1}^{n}{a_i^2}}$ is the Euclidean norm. It is inside the hyperball for $<$ and outside for $>$.