I have a list of points $ (x_i, y_i) $ for $i = 1...n$. Is there an algorithm to determine if the union of the unit discs centered at these points is a superset of the unit disc centered at $(0, 0)$?
Informally, I'm about to draw a whole bunch of non-transparent filled circles and want to know if I really need to bother drawing all of them. Some of them may be covered by circles that I will draw later. All the circles are the same size so I can do some simple preprocessing to give them all radius 1 and I can move them around so that the circle that I might not need to draw is at $(0, 0)$.
To phrase it a different way, I have a list of quadratic inequalities of the form: $ \begin{aligned} x^2 + y^2 \leq 1 \\ (x - x_1)^2 + (y - y_1)^2 \geq 1 \\ (x - x_2)^2 + (y - y_2)^2 \geq 1 \\ (x - x_3)^2 + (y - y_3)^2 \geq 1 \\ ... \end{aligned} $ and need to determine if there is a point that satisfies all of them.