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

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Mohamad Harb
Mohamad Harb 2021-11-19
评论： Mohamad Harb 2021-11-19
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
  2 个评论
DGM
DGM 2021-11-19
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
Mohamad Harb 2021-11-19
Could you help with writing a code about that problem. I know it's underdefined but I want to give it a try.

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