How to check if two circles have common part?

Question

I have equasion to calculate area of two circles with common part.

Equasion common part

But actually I just need to know if two cirlces have common part or no. Is there simpler equasion for that task? Can't find anything for hours...

For example: Two circles

Answer 1

If one circle is centered at $(x_1,y_1)$ with radius $r_1$ and the other circle is centered at $(x_2,y_x)$ with radius $r_2$, then they have a common part if and only if

$$(x_1-x_2)^2+(y_1-y_2)^2\le(r_1+r_2)^2$$

Note, in the case of equality, the common part is a single point, where the two circles are tangent.

Answer 2

Calculating the distance between their centres, if it if less then the sum of the radii then they have a common part.

Answer 3

If $$d<r_1+r_2$$ where $r_1$ and $r_2$ are the radii of the two circles, and $d$ is the distance between their centers. If this inequality is true, then they contain an overlapping section.