How to find circle from data points

How do i detect circle,circle center and radius from my data points?

clear all;clc;
x=zeros(1,361);
y=zeros(1,361);

x=[-90:0.5:90];

for i=1:361
    if (1<=i && i<160)
        y(i)=0.2*x(i)+3;
    end
    if (161<=i && i<200)
        y(i)=-sqrt(10^2-(x(i)^2));
    end
    if (201<=i && i<361)
        y(i)=-0.2*x(i)+3;
    end
end

figure
plot(x,y,'b.')
axis equal

Answer 1

[Andrei Bobrov]

dy = diff(y,2);
idx = find(abs(dy) > 1e-10)+1;
idc = idx(5)+(0:2:4);
id = [x(idc)',y(idc)'];
f = @(x,y)(y(:,1)+x(1)).^2+(y(:,2)+x(2)).^2 - x(3).^2;
xabr = fsolve(@(x)f(x,id),[0 0 1]').*[-1; -1;  1];

xabr(1:2) % coordinate of center circle [x;y]
x(3) % radius  circle