particle distributed on a ring

I want to generate a ring distribution of particles. This is my code so far

function [x,y]=cirrdnPJ(x1,y1,rc)

%the function, must be on a folder in matlab path
a=2*pi*rand;
r=sqrt(rand);
x=(rc*r)*cos(a)+x1;
y=(rc*r)*sin(a)+y1;
end

%to test the function
clf
axis equal
hold on
x1=1;
y1=1;
rc=1;
[x,y,~] = cylinder(rc,200);
plot(x(1,:)+x1,y(1,:)+y1,'r');
x1=1;
y1=1;
rc2=2;
[x,y,~] = cylinder(rc2,200);
plot(x(1,:)+x1,y(1,:)+y1,'p');
for t=1:1000 %loop until doing 1000 points inside the circle
[x ,y]=cirrdnPJ(x1,y1,rc2-rc);
plot(x,y,'x')
pause(0.01) %if you want to see the point being drawn
end

however the marks are appearing inside inner circle and not between two circles as I want. Any help or suggestion would be appreciated.

Answer 1

[KSSV]

clc ; clear all ;
r0 = 0.5 ;  % inner radius
r1 = 1. ;   % outer radius
% circles
th = linspace(0,2*pi) ;
x0 = r0*sin(th) ; y0 = r0*cos(th) ;
x1 = r1*sin(th) ; y1 = r1*cos(th) ;
plot(x0,y0,'r') ;
hold on
plot(x1,y1,'r') ;
%%generate random numbers
x = [x1 NaN fliplr(x0)] ;
y = [y1 NaN fliplr(y0)] ;
a = -1;
b = 1;
count = 0 ;
n = 0 ;   % number of pints lying inside 
while count==0
    r = (b-a).*rand(1,2) + a;
    idx = inpolygon(r(1),r(2),x,y) ;
    if idx
        plot(r(1),r(2),'.g')
        n = n+1 ;
    else
        plot(r(1),r(2),'.b')
    end
    drawnow
end

[Mamuna Anwar]

Thanks a lot for a quick response. This seems to work, however my goal is not only to get a plot but a distribution function that I can use as an input for another code. Can you please give any suggestion or help for this?