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);
[in,on] = inpolygon(x1, y1, x2, y2); % Find (x1,y1) In Or On (x2,y2)
inon = in | on;
figure
plot(x1,y1, x2, y2)
hold on
hinon = plot(x1(inon),y1(inon), 'pg'); % (x1,y1) In Or On (x2,y2)
hout = plot(x1(~inon),y1(~inon), 'pm') % (x1,y1) Outside (x2,y2)
hold off
legend([hinon,hout], '(x1,y1) In | On (x2,y2)', '(x1,y1) Outside (x2,y2)', 'Location','SE')
I am not certain what you intend with ‘after intersection point’, so I included both options (inside and outside the ellipse), and displayed them with different-colored pentagrams.
