Finding the intersection of a bunch of circles of different centers and radii, using FSOLVE

Write a Matlab routine to find the intersection of a bunch of circles of different centers and radii. You should expect around 5 to 10 circles, and also anticipate that the intersection may not be perfect, we use the data for the 5 circles centers and radii given in the table provided. How am i meant to solve this, we were told to use either fsolve or lsqnonlin, if someone could help me produce a code for this much will be appreciated

[Matt J]

How am i meant to solve this, we were told to use either fsolve or lsqnonlin

If you were told which command to use, isn't the "how" of it already answered?

[Nikunj Patel]

Sorry i meant what would the code look like, im new to matlab

Answer 1

[darova]

If circles normally intersect each other they have 2 intersection points

- equation for the first circle

- equation for the second

Dont know if fsolve() can find intersection point for this:

For example, code for lines intersection using fsolve():

clc, clear, cla
x = [0 4];
k1 = 1;
k2 = 3;
y1 = k1.*x+2;
y2 = k2.*x;
F = @(x) [x(2) - k1*x(1)-2
          x(2) - k2*x(1)];
x0 = [0 0];
xx = fsolve(F,x0);
hold on
plot(x,y1)
plot(x,y2)
plot(xx(1),xx(2),'or')
hold off

[Nikunj Patel]

how would i do it in this case, im still struggling

[darova]

You have 5 circles. If you want to compute intersection of the first two - draw them first to see where they intersect (more or less) for initial guess

clc, clear
t = linspace(0,2*pi,50);
x1 = -7.37 + 7.8*cos(t);
y1 =  7.65 + 7.8*sin(t);
x2 = 3.51 + 5.6*cos(t);
y2 = 1.05 + 5.6*sin(t);
plot(x1,y1,x2,y2)