3 Intersecting lines point, triangulation.

Question

I currently have 3 circles that intersect each other. At these points I create a line, although I am stumped at how I can find the point of which all 3 lines intersect?

I know the coordinate center of each circle as well as its radius and each of the lines start and end coordinate points.

I have tried following some other intersecting line posts and maths but haven't managed to fully understand the principles behind them.

Hope someone could find a solution and explain the process please?

Thanks,

Marc.

Answer 1

Subtracting the equations of two circles gives a linear equation.

Answer 2

If you know the coordinates of the line ends then you can work out the coordinate where they cross over and ignoring the circles? (I can't comment)

Answer 3

I'm trying to solve something similar also. By knowing the distance (d) from the intersection point(A,B) to each circle midpoint and respective midpoints coordinate (X,Y), you can try use the circle equation

(X1-A)^2 + (Y1-B)^2 = d1
(X2-A)^2 + (Y2-B)^2 = d2
(X3-A)^2 + (Y3-B)^2 = d3

This site - here solved the equation for coordinate (A,B).

I tried plot in an excel, it works. But I am figuring what's the explanation when all x-axis or y-axis align at the same level, the result will be undefined. Appreciate if anyone know about it.