# How can I plot a circle use given point?

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Seong-Won Ham on 25 Jan 2021
Commented: weikang zhao on 25 Jan 2021
I want to plot a circle, use given data.
but, I just know the some of the point in circle, but do not midpoint and radius.
Then, How Can I plot the circle using a given point?

KSSV on 25 Jan 2021
If you have points.....you can find the radius of circle. It depends on how many points you know.
Frame the distance formula and solve the equations.

weikang zhao on 25 Jan 2021
If you have coordinates of three points, the radius and center of the circle can be obtained by solving a positive definite equation set. If you have more points, there will be a overdetermined set, the midpoint and radius have a least squares estimation.
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weikang zhao on 25 Jan 2021
give you a demo:
clear
c=[5;5];%real coordinate of midpoint
pointNum=20;%num of all the points
thetatrain=unifrnd(0,2*pi,1,pointNum);
rtrain=r+0.01*randn(1,pointNum);
xytrain=c+[rtrain.*cos(thetatrain);rtrain.*sin(thetatrain)];%Generate a set of points perturbed around the circle
plot(xytrain(1,:),xytrain(2,:),'.');
A=[xytrain.',ones(pointNum,1)];
b=sum(xytrain.^2).';
est=(A.'*A)\A.'*b;
rhat=sqrt(est(1)^2/4+est(2)^2/4+est(3));%LS estimate of radius
xhat=est(1)/2;%LS estimate of the x coordinate of midpoint
yhat=est(2)/2;%LS estimate of the y coordinate of midpoint
hold on;
plot(xhat+rhat*cos(0:pi/180:2*pi),yhat+rhat*sin(0:pi/180:2*pi));
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