Please find below the code that results in the screenshot below.
How do I get Matlab to tell me the intersections of the two circles?

thanks in advance

clear % all variablesfigure(1), hold offset(gca,'FontSize',14) % adjust fontsizetext(0,10,'\leftarrow RX2 (x3,y3)=(0,10)','VerticalAlignment','middle','HorizontalAlignment','left')text(0,0,'\leftarrow RX1 (x3,y3)=(0,0)','VerticalAlignment','middle','HorizontalAlignment','left')center4=[0,0];radius4=11;N4=100; % number of points (circle resolution)hold onH=circle(center4,radius4,N4,'r-');center5=[0,10];radius5=1;N5=100; % number of points (circle resolution)hold onH=circle(center5,radius5,N5,'r-');center6=[0,0];radius6=15;N6=100; % number of points (circle resolution)hold onH=circle(center6,radius6,N6,'r-');center7=[0,10];radius7=5;N7=100; % number of points (circle resolution)hold onH=circle(center7,radius7,N7,'r-');

I think you might do a lot better with graph paper and a compass.
You should be able to see where the intersections are by eye well enough for this exercise.
You want to find enough points that you

Do you really need a code for this? Can you see the intersections by eyes?

Let me give you this code, so you can set the intersections manually so see them clearly. Paste it at the end of your drawing code. You will see a cross cursor on the figure. Click on the circles intersections you need. When you finish press Enter.
You can change line color and width as well as marker type and size as you wish.

I have attached in the code box below. Can you please have a look and see what I am doing wrong?

clear % all variablesfigure(1), hold offset(gca,'FontSize',14) % adjust fontsizetext(0,10,'\leftarrow RX2 (x3,y3)=(0,10)','VerticalAlignment','middle','HorizontalAlignment','left')text(0,0,'\leftarrow RX1 (x3,y3)=(0,0)','VerticalAlignment','middle','HorizontalAlignment','left')center4=[0,0];radius4=11;N4=100; % number of points (circle resolution)hold onH=circle(center4,radius4,N4,'r-');center5=[0,10];radius5=1;N5=100; % number of points (circle resolution)hold onH=circle(center5,radius5,N5,'r-');center6=[0,0];radius6=15;N6=100; % number of points (circle resolution)hold onH=circle(center6,radius6,N6,'r-');center7=[0,10];radius7=5;N7=100; % number of points (circle resolution)hold onH=circle(center7,radius7,N7,'r-');[X0,Y0] = intersections(0,0,0,10,true)

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No, X1, Y1,X2 and Y2 are not the centers of your circles. Those are vectors for X and Y data of your curves that are circles itself. You need to extract them from your circles. Here is the code for one circle.
Note as I found sometimes it actually misses an intersection when curves just touch each other.

I tried as per the code box but the text is distorted and also is it possible to get the coordinates printed on the screen?

clear % all variablesfigure(1), hold offset(gca,'FontSize',14) % adjust fontsizetext(0,10,'\leftarrow RX2 (x3,y3)=(0,10)','VerticalAlignment','middle','HorizontalAlignment','left')text(0,0,'\leftarrow RX1 (x3,y3)=(0,0)','VerticalAlignment','middle','HorizontalAlignment','left')center4=[0,0];radius4=11;N4=100; % number of points (circle resolution)hold onH1=circle(center4,radius4,N4,'r-');center5=[0,10];radius5=1;N5=100; % number of points (circle resolution)hold onH2=circle(center5,radius5,N5,'r-');center6=[0,0];radius6=15;N6=100; % number of points (circle resolution)hold onH3=circle(center6,radius6,N6,'r-');center7=[0,10];radius7=5;N7=100; % number of points (circle resolution)hold onH4=circle(center7,radius7,N7,'r-');X1=get(H1,'XData');Y1=get(H1,'YData');X2=get(H2,'XData');Y2=get(H2,'YData');X3=get(H3,'XData');Y3=get(H3,'YData');X4=get(H4,'XData');Y4=get(H4,'YData');[X01,Y01] = intersections(X1,Y1,X2,Y2,1);[X02,Y02] = intersections(X3,Y3,X4,Y4,1);text(X01,Y01,'\leftarrow intersection', 'VerticalAlignment','middle','HorizontalAlignment','left')text(X02,Y02,'\leftarrow intersection', 'VerticalAlignment','middle','HorizontalAlignment','left')

I think you might do a lot better with graph paper and a compass.
You should be able to see where the intersections are by eye well enough for this exercise.
You want to find enough points that you can draw the locus. There is a predictable pattern.
The real goal is develop some intuition. Matlab may be getting in the way.

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