Create circle that has random "noisy" points along circumference within 10% of circle radius

I need to create a circle of radius=20, centered at x=0, y=0. I then need to create random points along the circumference that may occur within +/-10% of the circles radius.

The image above is an example of what im trying to create.

Im fairly new to matlab, this is the code i have so far

%create circle 
r=20; %mm


%// center
c = [0 0];

pos = [c-r 2*r 2*r];
rectangle('Position',pos,'Curvature',[1 1])
axis equal

And this is the code ive tried to make random points within +/-10% of a r=20 circle

x0=0; % x0 and y0 are center coordinates
y0=0;  
r=20;  % radius mm
angle=-pi:0.1:pi;
angl=angle(randi(numel(angle),150,1))
x=r*cos(angl)+x0
y=r*sin(angl)+y0
scatter(x,y)
xlim([-r-1 r+1]+x0)
ylim([-r-1 r+1]+y0)
axis square

Its close to what im trying to get but its just generating random points directly on the circumference i think.

Is there also a way I can make a seed for the random points along the circumference so that i can get comparable results?

I also need the "noise" points along the circumference to be asterisks, if thats possible. Any help or guidance would be greatly appreciated. I know this post is asking a lot, I'm just very confused and cant find any other question looking for the same or similar results.

[the cyclist]

Did you write the above code, or was it provided to you?

Pardon my skepticism, but it seems strange that you could figure out how to make a random angle, but not a random radius.

[Evan Mang]

I've had help

Answer 1

[Matt J]

You can use this circularFit.xysim() from this FEX package

https://www.mathworks.com/matlabcentral/fileexchange/87584-object-oriented-tools-for-fitting-conics-and-quadrics

close all

[x0,y0]=deal(0,0); %Center coordinates
radius=20;           %Circle radius
thetaSamps=linspace(0,360,120); %Sample angles in degrees

xy=circularFit.xysim([x0,y0], radius, thetaSamps, 0.1*radius); %Generate noisy samples

plot( circularFit(xy)  );