import base_pi;
size(8cm,0);

path cle=yscale(3)*((0,0){N}..(1,0){N}..cycle);
draw(cle);

pair a=(0.2,.3), b=(.75,-.1);
dot("$A$",a,S);
dot("$B$",b,S);
draw(a--b);

real[] itd=intersections(cle,a,b);
draw(subpath(cle,itd[0],itd[2]), 1mm+.8blue);
draw(subpath(cle,itd[1],itd[2]), 1mm+.8green);
draw(subpath(cle,itd[2],length(cle)+itd[0]), 1mm+.8yellow);

/*<asyxml><view file="../base_pi.asy" type="pair[]" signature="intersectionpointsd(path,pair,pair)"/></asyxml>*/
pair[] pta=intersectionpointsd(cle,a,b);
dot(pta,red);
draw(pta[0]--a^^b--pta[1],red+dotted);