// Coordinates System :
SetCoords(579.3513427019788,371.1483383964919,186.4539962562527);


// Geometry :
E9=Expression("E9","x0 est calcul\u00e9 par l'expression ci-dessous (par dichotomie)","","","4","-2.9999429024478257","0.8642793484298292");
O=Point("O","[0,0]","0");
f=Expression("f","","","","sin(x)-x*cos(x)-\u03C0/2","-2.9999429024478257","1.078809478130166");
P3=Point("P3",5.483618877761174,-2.677858309856605);
E4=Expression("E4","Le probl\u00e8me de la ch\u00e8vre","","","1","-2.9999429024478257","1.8296649320813447");
A=Point("A","[-1,0]","0");
E8=Expression("E8","L'angle solution x0 est tel que 2x0 (angle NAM) soit solution de f(x)=0","","","3","-2.9999429024478257","1.2397070754054185");
E7=Expression("E7","la ch\u00e8vre broute la moiti\u00e9 du champ circulaire (ici de rayon 1)","","","2","-2.9999429024478257","1.4006046726806711");
E6=Expression("E6","On cherche \u00e0 d\u00e9terminer la longeur de la corde pour que ","","","3","-2.9999429024478257","1.5078697375308396");
E10=Expression("E10","M est aimant\u00e9 par la solution ","","","3","-2.9999429024478257","-0.47653396219727556");
E5=Expression("E5","Une ch\u00e8vre est attach\u00e9e \u00e0 une corde en M \u00e0 partir d'un piquet A","","","2","-2.9999429024478257","1.668767334806092");
x0=Expression("x0","x0 = ","","","var a=1;var b=2;while(b-a>0.000000000001){c=(a+b)/2;if(f(c)<0){a=c;} else {b=c;}};(a+b)/4","-2.9999429024478257","0.7033817511545767");
Symc1=Symmetry("Symc1",O,A);
C7=Circle("C7",A,O);
C1=Circle("C1",O,A);
E1=Expression("E1","V\u00e9rification f(2*x0) = ","","","f(2*x0)","-2.839045305172573","0.4352190890291557");
S1=Segment("S1",A,Symc1);
P1=Point("P1","[-1+cos(x0),0]","0");
M=PointOn("M",C1,4.702368358800344);
asol=Expression("asol","","","","x0*180/\u03C0","-2.9999429024478257","0.11342389447865053");
C2=Circle("C2",A,M);
S2=Segment("S2",A,M);
anglO=Angle("anglO",A,O,M);
Perp1=Perpendicular("Perp1",S1,P1);
anglA=Angle("anglA",Symc1,A,M);
P2=OrderedIntersection("P2",Perp1,C7,0);
U=OrderedIntersection("U",S1,C2,0);
N=OrderedIntersection("N",C2,C1,1,M);
MONA=Polygon("MONA","_A,_N,_O,_M");
C3=Arc3pts("C3",M,U,N);
Symc2=Symmetry("Symc2",A,U);
C4=Arc3pts("C4",N,A,M);
C5=Arc3pts("C5",M,Symc1,N);
R1=Ray("R1",A,P2);
Center3=Center("Center3",C4);
C6=Arc3pts("C6",N,Symc2,M);
Center1=Center("Center1",C5);
aCh=Expression("aCh","aire verte =","","","(anglA*d(A,M)^2+(2*\u03C0-anglO))*(y(M)>0)+((2*\u03C0-anglA)*d(A,M)^2+anglO)*(y(M)<0)-MONA","-2.9463103700227413","-0.10110623522168624");
Msol=OrderedIntersection("Msol",R1,C1,0,A);
Center2=Center("Center2",C3);
E2=Expression("E2","aire verte - \u03c0/2 = ","","","aCh-\u03C0/2","-2.9999429024478257","-0.315636364922023");
Msol2=Reflection("Msol2",S1,Msol);
Center4=Center("Center4",C6);
gdP=Expression("gdP","","","","(d(M,Msol)==0) || (d(M,Msol2)==0)","-2.6781477078973204","-1.120124351298286");
E3=Expression("E3","","","","if(gdP==0){anglA.setPrecision(4);} else {anglA.setPrecision(9);};\"precision anglA\"","-2.7317802403224047","-1.3346544809986227");


// Styles :
STL(E9,"c:#931414;s:7;f:15;p:-1;cL:200;cPT:YzojNzgwMDEzO3M6MTA7ZjozMA==");
STL(O,"c:#0000b2;s:6;sn:true;f:20");
STL(f,"c:#2137b2;s:7;sn:true;f:18;p:4;cL:200;cPT:YzojNzgwMDEzO3M6MTA7ZjoyMA==");
STL(P3,"c:#0000b2;s:6;f:20");
STL(E4,"c:#0000b2;s:7;f:20;p:-1;cL:200;cPT:YzojNzgwMDEzO3M6MTA7ZjozMA==");
STL(A,"c:#0000b2;s:6;sn:true;f:20");
STL(E8,"c:#8d2c9b;s:7;f:16;p:-1;cL:200;cPT:YzojNzgwMDEzO3M6MTA7ZjozMA==");
STL(E7,"c:#966400;s:7;f:16;p:-1;cL:200;cPT:YzojNzgwMDEzO3M6MTA7ZjozMA==");
STL(E6,"c:#966400;s:7;f:16;p:-1;cL:200;cPT:YzojNzgwMDEzO3M6MTA7ZjozMA==");
STL(E10,"c:#b40000;s:7;f:18;p:-1;cL:200;cPT:YzojNzgwMDEzO3M6MTA7ZjozMA==");
STL(E5,"c:#2600ff;s:7;f:18;p:-1;cL:200;cPT:YzojNzgwMDEzO3M6MTA7ZjozMA==");
STL(x0,"c:#d60d0d;s:7;sn:true;f:18;p:11;cL:200;cPT:YzojNzgwMDEzO3M6MTA7ZjoyMA==");
STL(Symc1,"c:#0000b2;h:1;s:6;f:20");
STL(C7,"c:#cc66cc;h:1;s:1;f:30;p:0");
STL(C1,"c:#cc66cc;h:1;s:1;f:30;p:0");
STL(E1,"c:#3b4e4a;s:7;f:18;p:4;cL:200;cPT:YzojNzgwMDEzO3M6MTA7ZjoyMA==");
STL(S1,"c:#006633;s:1;f:24");
STL(P1,"c:#0000b2;h:1;s:6;f:30");
STL(M,"c:#b40000;o:1;s:6;sn:true;f:20;mg:[Msol,2],[Msol2,1]");
STL(asol,"c:#410377;s:7;sn:true;f:18;p:9;cL:200;cPT:YzojNzgwMDEzO3M6MTA7ZjoyMA==");
STL(C2,"c:#cc66cc;h:1;s:1;f:30;p:0");
STL(S2,"c:#006633;s:1;f:24");
STL(anglO,"c:#006633;h:1;s:4;sn:true;f:24;p:1");
STL(Perp1,"c:#780013;h:1;s:1;f:30;p:0");
STL(anglA,"c:#006633;s:4;sn:true;f:24;p:4");
STL(P2,"c:#0000b2;h:1;s:6;f:30");
STL(U,"c:#0000b2;h:1;s:6;sn:true;f:20");
STL(N,"c:#0000b2;s:6;sn:true;f:20");
STL(MONA,"c:#006633;h:1;o:0.2;s:1;sn:true;f:30");
STL(C3,"c:#007c7c;o:0.16;s:1;f:30;p:0");
STL(Symc2,"c:#0000b2;h:1;s:6;f:20");
STL(C4,"c:#007c7c;o:0.16;s:1;f:30;p:0");
STL(C5,"c:#0035ff;s:1;f:30;p:0");
STL(R1,"c:#993300;h:1;s:1;f:30;p:0");
STL(Center3,"c:#0000b2;h:1;s:6;f:20");
STL(C6,"c:#cc66cc;s:1;f:30;p:0");
STL(Center1,"c:#0000b2;h:1;s:6;f:20");
STL(aCh,"c:#471e30;s:7;sn:true;f:18;p:7;cL:200;cPT:YzojNzgwMDEzO3M6MTA7ZjozMA==");
STL(Msol,"c:#b40000;h:1;s:6;sn:true;f:17;sp:1;np:2.1109043743485256");
STL(Center2,"c:#0000b2;h:1;s:6;f:20");
STL(E2,"c:#40664b;s:7;f:18;p:4;cL:200;cPT:YzojNzgwMDEzO3M6MTA7ZjozMA==");
STL(Msol2,"c:#b40000;h:1;s:6;sn:true;f:17;sp:1");
STL(Center4,"c:#0000b2;h:1;s:6;f:20");
STL(gdP,"c:#712762;h:1;s:7;sn:true;f:24;p:4;cL:200;cPT:YzojNzgwMDEzO2g6MTtzOjEwO2Y6MzA=");
STL(E3,"c:#1d521c;h:1;s:7;f:18;p:4;cL:200;cPT:YzojNzgwMDEzO2g6MTtzOjEwO2Y6MzA=");
SetCoordsStyle("isAxis:false;isGrid:true;isOx:true;isOy:true;isLockOx:false;isLockOy:false;centerZoom:false;color:#111111;fontSize:18;axisWidth:1;gridWidth:0.1");