Two circles intersect if, and only if, the distance between their centers is between the sum and the difference of their radii. Given two circles `(x0, y0, R0)`

and `(x1, y1, R1)`

, the formula is as follows:

```
ABS(R0 - R1) <= SQRT((x0 - x1)^2 + (y0 - y1)^2) <= (R0 + R1)
```

Squaring both sides lets you avoid the slow `SQRT`

, and stay with ints if your inputs are integers:

```
(R0 - R1)^2 <= (x0 - x1)^2 + (y0 - y1)^2 <= (R0 + R1)^2
```

Since you need only a yes/no test, this check is faster than calculating the exact intersection points.

The above solution should work even for the “one circle inside the other” case.