how to get intersection point of two curves?

I want to get intersect point of two curve. I am use InterX for intersection of curves but I get error which is attacted below.

%program 

syms Rb
R1=200;
R3=100;
R2=(R1+R3)/2;
theta=135;
Rb=solve((tan(acos(Rb/R1))-tan(acos(Rb/R2))-(acos(Rb/R1))+(Rb/R2))*(180/pi)==180-theta,Rb);
disp(Rb)
alpha=(tan(acos(Rb/R2))-acos(Rb/R2))*(180/pi);
disp(alpha)
t=linspace(0,2*pi);
x1=Rb*(cos(t-alpha)+t.*sin(t-alpha));
y1=Rb*(sin(t-alpha)-t.*cos(t-alpha));
x2=R1*cos(t);
y2=R1*sin(t);
plot(x1,y1,x2,y2)
hold on
q1=InterX([x1;y1],[x2;y2])
plot(x1,y1,x2,y2,P(1,:),P(2,:),'ro')

%error

140.5685985955217381715139492076

0.9117041268384028699662544052952

Error using symengine (line 59)
Array sizes must match.

Error in sym/privBinaryOp (line 903)
            Csym = mupadmex(op,args{1}.s, args{2}.s, varargin{:});

Error in  .*  (line 238)
        X = privBinaryOp(A, B, 'symobj::zip', '_mult');

Error in InterX (line 60)
    S1 = dx1.*y1(1:end-1) - dy1.*x1(1:end-1);

Error in solve_equation (line 40)
q1=InterX([x1;y1],[x2;y2])

Answer 1

[Star Strider]

Try this:

syms Rb
R1=200;
R3=100;
R2=(R1+R3)/2;
theta=135;
Rb=vpasolve((tan(acos(Rb/R1))-tan(acos(Rb/R2))-(acos(Rb/R1))+(Rb/R2))*(180/pi)==180-theta,Rb);
disp(Rb)
alpha=(tan(acos(Rb/R2))-acos(Rb/R2))*(180/pi);
disp(alpha)
t=linspace(0,2*pi);
x1=Rb*(cos(t-alpha)+t.*sin(t-alpha));
y1=Rb*(sin(t-alpha)-t.*cos(t-alpha));
x2=R1*cos(t);
y2=R1*sin(t);
x1 = double(x1);
y1 = double(y1);
x2 = double(x2);
y2 = double(y2);

plot(x1,y1,x2,y2)
hold on
% q1=InterX([x1;y1],[x2;y2])
[D,I] = pdist2([x1;y1]',[x2;y2]','euclidean','Smallest',1);
[minD,idx] = min(D);
P = [x1(I(idx)); y1(I(idx))];
plot(x1,y1,x2,y2,P(1,:),P(2,:),'ro')

It uses the pdist2 function to return the smallest distance between the points in the two sets, approximating the intersection.

[Bruno Luong]

This curve intersection FEX is perhaps better than pdist2.

[Star Strider]

I wanted to see if I could code an acceptable alternative using built-in functions.

[Bruno Luong]

polyxpoly but it requires the Mapping toolbox. Without the toolbox you might end up doing what this FEX does.