How to find out circumference of circle with given centres and radius is completely covered by other intersecting circles with same radius

Question

I want to find whether the circumference of a circle with given centre and radius is completed covered by two or more circles with given centre and same radius in matlab

Answer 1

Let $\gamma$ be the initial circumference and $\Gamma_1,\ldots,\Gamma_n$ the given circles, with centers $O_1,\ldots,O_n$. Assuming that $\Gamma_1$ intersects $\gamma$, let $$\gamma_1=\gamma\setminus\Gamma_1$$ and $A_1$ be one of the endpoints of $\gamma_1$. Relabel $\Gamma_2,\ldots,\Gamma_n$ in such a way that $O_2$ is the closest point to $A_1$ among $O_2,\ldots,O_n$, then set $\gamma_2=\gamma_1\setminus\Gamma_{2}$ and iterate until $\gamma_k$ is empty or $k=n$.