Omar Kháyyám

 input courbes;
 %% ======================================== fonction(s)
 vardef fx(expr t) =
         t
 enddef;
 vardef fy(expr t) =
         t*t/2
 enddef;
 %% ======================================== figure(s)
 

 beginfig(1)
         repere(6cm,6cm,2cm,1cm,1cm,1cm);
         trace.axes(1pt);
         path parabole, cercle;
         parabole = ftrace(-2,4,20) scaled 1cm shifted origine;
 	cercle = fullcircle rotated -80 scaled 3cm shifted (3.5cm,1cm);
 	z1 = ((parabole cutbefore ((1cm,0.5cm) shifted origine)) intersectionpoint cercle);
         z2 = (x1,1cm);
 	z3 = (3cm,0) shifted origine;
 	draw parabole;
 	draw cercle;
 	draw z1--z2;
         pickup pencircle scaled 1pt;
         draw origine--z2 withcolor red;
         dotlabel.ulft(btex $P$ etex,z1);
         dotlabel.llft(btex $Q$ etex,z2);
 	dotlabel.llft(btex $A$ etex,z3);
 	dotlabel.llft(btex $O$ etex,origine);
         decoupe.repere;
 endfig;
 end