Q:

Draw a circle inside a convex hull with its centre at the origin

I am trying to draw a circle inside a convex hull with its center at the origin. I have attached the code generating the points and the convex hull. In what way can I generate the incircle with its center at the origin.
A=[0 0;0 -5; 5 -5; 5 5;0 5;-2 2;-5 -5;5 8;-5 -8;-8 0;8 0]
x_axis=A(:,1)
y_axis=A(:,2)
k=convhull(x_axis,y_axis);
figure;
plot(x_axis(k),y_axis(k),'r-',x_axis,y_axis,'b*');

Trying to get a circle inscribed like this. With its center at the origin. ( drawing edited in paint, not matlab) 

A:

Find the min distance from center(origin) to all edges and plot the circle.
clear all;

A=[0 0;0 -5; 5 -5; 5 5;0 5;-2 2;-5 -5;5 8;-5 -8;-8 0;8 0]
x_axis=A(:,1)
y_axis=A(:,2)
k=convhull(x_axis,y_axis);
figure;
hold on
plot(x_axis(k),y_axis(k),'r-',x_axis,y_axis,'b*');

Centre = [0 0 0];
ConvexHull = [x_axis(k) y_axis(k) zeros(size(k))];

radius = Inf;
for i = 1:size(k)-1
    radius = min(radius,Distance(Centre, ConvexHull(i,:), ConvexHull(i+1,:)));
end
radius = min(radius,Distance(Centre, ConvexHull(1,:), ConvexHull(size(k),:)));

viscircles([0 0],radius);

function d = Distance(pt, v1, v2)
      a = v1 - v2;
      b = pt - v2;
      d = norm(cross(a,b)) / norm(a);
end

Add axis equal if the axes don't have same scale.
viscircles

