I guess your problem is to find the two points of intersection between p and r ? If so, the problem is that intersectionpoint does return the same intersection when there is several, as it is the case here. So a quick solution that you can do is to find intersections for the two part. A drawing is simple than words ! here is the code to illustrate:

\setupcolors[state=start]

\starttext

\startMPpage

path p, q, r, b , u;

p:= fullcircle scaled 6cm ;

q:= fullcircle scaled 4cm shifted (2.5cm,2cm) ;

r:= fullcircle scaled 4cm shifted (-2.5cm,2cm);

b:= fullcircle scaled 2cm shifted (0,-3cm);

pair A, B ;

path rprime ;

% Rprime is a a part of r (drawn in black to see it):

rprime := r cutbefore point .5 along r;

A:= p intersectionpoint r ;

B:= p intersectionpoint rprime ;

draw A withpen pencircle scaled .1in ;

draw B withpen pencircle scaled .1in ;

u:= A--B--cycle ;

draw p withcolor green;

draw q withcolor blue;

draw rprime withpen pencircle scaled .05in withcolor black;

draw r withcolor red;

draw b withcolor magenta;

draw u numberstriped (.25,15,5) withcolor magenta ;

\stopMPpage

\stoptext

Hi,
I would like to reproduce the attached figure. My problem is to create the points of intersection between the circles. It seems that my approach is not the right one.
Thank you.
Fabrice

\starttext
\startMPcode
path p, q, r, b ;
p:= fullcircle scaled 6cm ;
q:= fullcircle scaled 4cm shifted (2.5cm,2cm) ;
r:= fullcircle scaled 4cm shifted (-2.5cm,2cm);
b:= fullcircle scaled 2cm shifted (0,-3cm);
pair A, B ;
A:= p intersectionpoint r ;
B:= p intersectionpoint r ;
path u ;
u:= A--B--cycle ;
draw p ;
draw q ;
draw r ;
draw b ;
draw u numberstriped (.25,15,5) withcolor magenta ;
\stopMPcode
\stoptext

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