How to solve 2 non linear circle equations with vector inputs?

So I have 2 circles that intersect and im trying to solve for those intersection points but also the larger circle in this case f(1) or the circle with the C variables has a variable centre. The centre of the larger circle has different postions on a path and im aiming to find the intersection points as the larger cricle moves. Here is my function:

function f=f_lower(x)

xx=x(1);

yy=x(2);

%the displacement in vector form

dy=linspace(-20,59);

yl0=103.3;

yl1=yl0+dz;

hl0=20;

kl0=103.3;

CD=485.6445;

%the path the centre follows is also an arc

xl1=sqrt((CD^2)-((yl1-kl0).^2))+hl0;

%the new centre values

Ch=xl1;

Ck=yl1;

Cr=542.206;

%smaller cirlce centres/radius

Gh=240.941;

Gk=576.502;

Gr=68.75;

f(1)=(Cr^2)==((xx-Ch).^2)+((yy-Ck).^2);

f(2)=(Gr^2)==((xx-Gh)^2)+((yy-Gk)^2);

end

And then my function in the editor is:

fun=@f_lower;

fsolve(fun,[293.693,602.363])

I found my first intersection using desmos to get my "x0" value in the function for it to solve from.

Still it doesnt work and I can not see why. Any help would be great.

Answer 1

[Torsten]

f(1)=(Cr^2)-((xx-Ch)^2)+((yy-Ck)^2);
f(2)=(Gr^2)-((xx-Gh)^2)+((yy-Gk)^2);

instead of

f(1)=(Cr^2)==((xx-Ch)^2)+((yy-Ck)^2);
f(2)=(Gr^2)==((xx-Gh)^2)+((yy-Gk)^2);