# how can i styling overlapping part of two circles with filling of hatching?

hi,

thanks for the great tool to engage math teaching.

How can i styling overlapping section of two circles with filling of hatching?

Currently, i can only see different color lightness or hue changed bit. But i want to style it with hatching filling. How can i implement that? Is there any workaround solution for it?

thanks.

3

Hi,

- for the top semi circle, you can use a circularsector that can be filled

- for other domains, you can

• create 2 circular arcs
• create a free M point on the sequence of 2 such circular arcs
• create MM=M just to create a locus MM from M
• you can fill or hatch the domain of the locus with the style

2

arc: CircularArc(centre,point,point)

1

hi, Michel, currently i have understood your approach of locus for this problem. It is perfect and beautiful and can work for many situations. Great! thanks~

3

I like this way

Files: foro.ggb
1

hi, mathmagic,

If the overlapped region is a semi-circle, can we use your approach of inequality?

1

using the circle c with the diametral line (not vertical) e.g. f(x)=2x+3, just do the intersect of the domains (inequation of the semi-plane and the inequation of the disk related by && (that yields ^)) like that :

(y>=f(x))&&(LeftSide(c)<=RightSide(c))

LeftSide(c)<=RightSide(c) <=> CM^2<= r^2 <=> CM<= r with C the center and r the ray

1

for this case you can use semicircle trough 2 points also (it is valid for vertical diameters)

1

@mathmagic, assumming k=semicircle through 2 points, but following expression is not valid:

LeftSide(k)<RightSide(k)

Is there some workaround solution?

1

@Michel, thank you so much for your effort helping me! Can you give a solution based on inequality approach for this final product in the attachment?

thanks

1

With intersections of domains

1

thanks, michel, i caught it

1

thank you very much. You helped me out one day~. I like @mathmagic way. It is simple and just work.

I am a new hand, solution from Michel and alfabeta2 works well, but i can not understand well. I will do more study and understand these solutions. thanks again~

1

my solution using a custom tool:

https://ggbm.at/XmvnxSZT

1

some usefull figures without inequality

Files: foro.ggb