I struggle with the following problem:

Given $N$ disks $D\_i = (x\_i, y\_i,r\_i)$, calculate whether they ALL intersect. 

$D\_1 \cap D\_2 \cap \dots \cap D\_N = \emptyset $ ?

I do not care about the intersection area, just want to know whether they do or not.

I know how to check whether two disks intersect.
I read 

[the intersection of n disks/circles](https://math.stackexchange.com/questions/221881/the-intersection-of-n-disks-circles)

But their algorithm seems to be not 100% accurate, since floating point arithmetics and focused on the calculation of the resulting area.

I thought about representing disks as a set, like: 

```
The set of all points equidistant from the center,

```

but that does not help me too much. My idea was, given a point $p$, 

all $N$ disks intersect $ \iff \exists \ p: p \in D\_1 \wedge p \in D\_2 \wedge \dots \wedge p \in D\_N $,

but the only way to implement that into code that comes to my mind is to use Monte Carlo, and that is (maybe) slow and not accurate either.

Does somebody know a fast and hopefully easy solution?

**Edit: Changed from circles to disks, after it was pointed out that I mean disks.**