Having two touching circles, find the third one so it's touching both

I gave it a try but I can't get the answer. any help please

function [] = circle()

x1=input('Enter the value of x1: ');

x2=input('Enter the value of x2: ');

y1=input('Enter the value of y1: ');

y2=input('Enter the value of y2: ');

r1=input('Enter the value of r1: ');

r2=input('Enter the value of r2: ');

%Consider the triangle C1C2C3

%BC3 = h = the altitude

%Pethagoran theorem: C3C1^2 - BC1^2=C3C2^2 - BC2^2 setting d=BC1

%(r3+r1)^2 - d^2 = (r3+r2)^2 - (r1+r2-d)^2

%d = (r1*(r3+r1)-r2*(r3-r1))/(r1+r2)

%h = sqrt((r3+r1)^2 - d^2)

%set vector u = C2-C1/r1+r2 (the unit vector that point from C1 to C2)

%set vector v = rot(u) = <-uy,ux> (vector u rotated 90 degrees

%counterclockwise)

%then C3 = C1 + du + hv

%C3 = C1 + (d/r1+r2)*(C2-C1) + (h/r1+r2)*rot(C2-C1) then use this equation

%for x3

syms r3 x3 y3

E1 = sqrt((x3-x1)^2 + (y3-y1)^2)-r1-r3==0;

E2 = sqrt((x3-x2)^2 + (y3-y2)^2)-r2-r3==0;

E3 = x1 - x3 + ((r1*(r3+r1)-r2*(r3-r1))/(r1+r2)^2)*(x2-x1) + ((sqrt((r3+r1)^2 - ((r1*(r3+r1)-r2*(r3-r1))/(r1+r2))^2))/(r1+r2))*(x2-x1) == 0;

S = solve(E1,E2,E3);

Center = [S.x3,S.y3];

disp(Center);

disp('radius = ') ,disp(S.r3)

end

[DGM]

There are issues, but let's back up first. You're trying to solve for the center and location of a circle that's tangent to two others. There are an infinite number of circles that can do that. It's an underdefined problem.

[Mohamad Harb]

Could you help with writing a code about that problem. I know it's underdefined but I want to give it a try.