Overlap circle outline

[414184]

Hello.

I have post threads before about trilateration and triangulation. This question will be about trilateration.
For trilateration i need three reference points and the distance to these reference points to find de position of an unknown node.

Therefore the circle outlines have to overlap each other. How can i check if two circles outlines in a Cartesian Coordinate System overlap each other? So i can verify the distances i measure are correct. So the trilateration algorithm will give me correct answers.

As example the image. How can i verify in a formula that outline of Node B has a intersection with Node A?
Thanks in advance!

 

[Deleted member 4993]

Hello.

I have post threads before about trilateration and triangulation. This question will be about trilateration.
For trilateration i need three reference points and the distance to these reference points to find de position of an unknown node.

Therefore the circle outlines have to overlap each other. How can i check if two circles outlines in a Cartesian Coordinate System overlap each other? So i can verify the distances i measure are correct. So the trilateration algorithm will give me correct answers.

As example the image. How can i verify in a formula that outline of Node B has a intersection with Node A?
Thanks in advance!

View attachment 20798

One way I can think of is as follows:

Calculate the distance (d) between the centers of the circles with radii r₁ and r₂.

If d < r₁ + r₂, the circles intersect.

 

[HallsofIvy]

You give the coordinates of the centers of the circles (the "nodes") but what are the radii of the circles?