Research problem (Q5917795)

The author defines a ``loose-covering'' of \(\mathbb{R}^2\) by circles \(C_i\), that is each point \(x\in \mathbb{R}^2\) lies in some \(C_i\), but at most in the interior of two of the \(C_i\), and the center of a circle is not contained in the interior of any other circle. He then gives an example of such a ``loose- covering'' by unit circles deriving a lower bound for the arc \(\Delta\) of certain triangles whose vertices are centers of the circles \(C_i\). He suggests that there is no denser ``loose-covering'' than the one he found.