How to Create Graded lines inside the binary circle mask?

I have a binary circle mask. and i need create new binary mask from that with Graded lines inside the circle.Degrees is 45,90,135,180. please guide me.

 clc; clear;
 %%create circle mask
 mask = zeros(400,600);
 position = [200,300];
 cx = position(1);
 cy = position(2);
 r = 50;
 [ix,iy] = size(mask);
 [x,y]=meshgrid(-(cx-1):(ix-cx),-(cy-1):(iy-cy));
 c_mask=((x.^2+y.^2)<=r^2)';
 figure,imshow(c_mask)
 %%Create Graded lines inside the circle.
 %find center of circle
 BW = c_mask;
 prob = regionprops(BW,'centroid');
 center = prob.Centroid;
 figure, imshow(BW)
  hold on
 plot(center(1),center(2),'rx','MarkerSize',18,'LineWidth',2);

Answer 1

[KSSV]

YOu decide the angles needed, and use this:

th = [45,90,135,180] ; 
 x = center(1)+r*cos(th) ; 
 y = center(2)+r*sin(th) ;
 for i = 1:length(th)
     plot([center(1) x(i)],[center(2) y(i)],'r')
 end

Note that, to draw line, loop is not required.

[fred bnm]

Thanks for your attention. if we suppose that we have one degree,to create new binary mask (not plot) with line,What should we do?

[KSSV]

Not clear.....can you elaborate?

[fred bnm]

i want create new mask using imwrite. but this code just plot.