// Coordinates System :
SetCoords(-69,8,86.15614953124279,true);


// Geometry :
O=Point("O",6.465005725424339,-6.140014414271947);
P4=Point("P4","[-4,4,0]","1");
P3=Point("P3","[4,-4,0]","1");
P19=Point("P19",9.168170514892564,-3.214488161428908);
P5=Point("P5","[-4,-4,0]","1");
E15=Expression("E15","lui m\u00eame modifiable, et N, P, Q, R sur la sph\u00e8re solution. ","","","7","0.9169397707513872","-1.8803068716674016");
E14=Expression("E14","On peut modifier les param\u00e8tres (curseurs), d\u00e9placer A, B, C sur le t\u00e9tra\u00e8dre ILKL, ","","","6","0.9169397707513872","-1.6481702208442657");
E13=Expression("E13","Q sur le parall\u00e8le \u00e0 l'\u00e9quateur passant par P et R sur un autre m\u00e9ridien. ","","","5","0.9169397707513872","-1.2999652446095615");
E12=Expression("E12","N est sur l'\u00e9quateur, P sur le m\u00e9ridien passant par N,  ","","","4","0.9169397707513872","-1.0678285937864256");
E10=Expression("E10","avec G=Bar{(A,a),(B,b),(C,c)} et r=sqrt((k-g(G))/(a+b+c)). ","","","3","0.9169397707513872","-0.7196236175517217");
E9=Expression("E9","Dans l'espace (a+b+c\u22600) c'est une sph\u00e8re de centre G et de rayon r, ","","","2","0.9169397707513872","-0.4874869667285856");
P20=Point("P20",1.1490764215745233,-2.9017081352892);
E5=Expression("E5","Fonction scalaire de Leibniz g(M)=aMA^2+bMB^2+cMC^2. Ligne de niveau g(M) = k","","","4","0.916939770751387","-0.1392819904938816");
P1=Point("P1",7.359630123314819,-2.4154402216035065);
X=Point("X","[1,0,0]","1");
P6=Point("P6","[4,4,6]","1");
Z=Point("Z","[0,0,1]","1");
Y=Point("Y","[0,1,0]","1");
E16=Expression("E16","Le tri\u00e8dre se d\u00e9place \u00e0 un doigt sur tablette, \u00e0 la souris sur ordinateur. ","","","8","0.9169397707513872","-2.112443522490538");
P2=Point("P2","[4,4,0]","1");
E17=Expression("E17","En ligne : http://goo.gl/5h2QzM ","","","2","1.1490764215745233","-7.335518166011098");
k=ExpressionOn("k","","-5","5","-3.153869669947517",P1,[30,60]);
S21=Segment("S21",O,Y);
S11=Segment("S11",O,X);
b=ExpressionOn("b","","-5","5","-0.11541074438612942",P1,[30,-40]);
S31=Segment("S31",O,Z);
Poly1=Polygon("Poly1","_P3,_P2,_P4,_P5");
c=ExpressionOn("c","","-5","5","-0.2548370874343959",P1,[30,10]);
S8=Segment("S8",P2,P6);
a=ExpressionOn("a","","-5","5","0.8076629125656041",P1,[30,-90]);
K=PointOn("K",Poly1,[0.2106967784531538,0.07621384977825138]);
I=PointOn("I",Poly1,[0.5216066465433008,0.37961398145956693]);
M=PointOn("M",S8,0.6261238817366982);
J=PointOn("J",Poly1,[-0.44294404085794226,0.749601891944198]);
angl25=Angle("angl25",I,J,K);
P8=Point("P8","[-4,-4,M[2]]","1");
P9=Point("P9","[4,-4,M[2]]","1");
S104=Segment("S104",K,J);
angl23=Angle("angl23",K,I,J);
angl24=Angle("angl24",J,K,I);
E1=Expression("E1","","","","[-4,4,M[2]]","6.2560827396835155","-2.112443522490538");
S103=Segment("S103",I,K);
P7=Point("P7","[-4,4,M[2]]","1");
S7=Segment("S7",P2,M);
S105=Segment("S105",J,I);
Poly2=Polygon("Poly2","_M,_P7,_P8,_P9");
L=PointOn("L",Poly2,[0.1546128692684389,2.732976239316742e-16]);
Poly3=Polygon("Poly3","_L,_J,_K");
angl1=Angle("angl1",J,I,L);
angl12=Angle("angl12",K,J,L);
S101=Segment("S101",K,L);
angl22=Angle("angl22",L,J,I);
S102=Segment("S102",J,L);
angl13=Angle("angl13",L,I,K);
S10=Segment("S10",I,L);
angl15=Angle("angl15",L,J,I);
angl2=Angle("angl2",L,I,K);
angl21=Angle("angl21",L,K,J);
angl11=Angle("angl11",I,K,L);
Poly5=Polygon("Poly5","_L,_K,_I");
angl14=Angle("angl14",L,K,J);
Poly4=Polygon("Poly4","_L,_I,_J");
A=PointOn("A",Poly4,[0.49948345442821374,0.23171139326882248]);
E34=Expression("E34","","","","S104.setDash((angl14>\u03C0)&&(angl24>\u03C0));\"Dash code\"","0.8008714453398192","-0.632633070182656");
E32=Expression("E32","","","","S102.setDash((angl12>\u03C0)&&(angl22>\u03C0));\"Dash code\"","1.8858334281879392","-0.5629920749357152");
C=PointOn("C",Poly5,[0.5781503816196408,0.2755127799011618]);
E35=Expression("E35","","","","S105.setDash((angl15>\u03C0)&&(angl25>\u03C0));\"Dash code\"","0.8008714453398192","-0.7022740654295967");
E31=Expression("E31","","","","S101.setDash((angl11>\u03C0)&&(angl21>\u03C0));\"Dash code\"","4.230413601501612","-0.5513852423945584");
E33=Expression("E33","","","","S103.setDash((angl13>\u03C0)&&(angl23>\u03C0));\"Dash code\"","1.7117309400705871","-0.5281715773122448");
E3=Expression("E3","","","","S10.setDash((angl1>\u03C0)&&(angl2>\u03C0));\"Dash code\"","3.3018669982090687","-0.574598907476872");
B=PointOn("B",Poly3,[0.18351596857806446,0.38309726325721843]);
G=Point("G","(a*A+b*B+c*C)/(a+b+c)","1");
S1=Segment("S1",O,B);
S2=Segment("S2",O,A);
P10=Point("P10","(A+B+C)/3","1");
Symc2=Symmetry("Symc2",P10,A);
CdG=Expression("CdG","","","","G","1.2651447469860913","-5.246288308602874");
Symc6=Symmetry("Symc6",G,P19);
Symc3=Symmetry("Symc3",P10,B);
gG=Expression("gG","g(G) = ","","","a*d(A,G)^2+b*d(B,G)^2+c*d(C,G)^2","7.532834319210763","-0.6035552921401536");
Symc1=Symmetry("Symc1",P10,C);
r=Expression("r","","","","sqrt((k-gG)/(a+b+c))","7.532834319210763","-0.9517602683748576");
Poly6=Polygon("Poly6","_Symc3,_A,_Symc1,_B,_Symc2,_C");
E2=Expression("E2","","","","[G[0]+r,G[1],G[2]]","1.0330080961629553","-1.5321018954326977");
P12=Point("P12","[G[0],G[1]+r,G[2]]","1");
P13=Point("P13","[G[0],G[1],G[2]+r]","1");
P14=Point("P14","[G[0]+r/2,G[1]+sqrt(3)*r/2,G[2]]","1");
P11=Point("P11","[G[0]+r,G[1],G[2]]","1");
Symc5=Symmetry("Symc5",G,P12);
S3=Segment("S3",G,P11);
S5=Segment("S5",G,P13);
S4=Segment("S4",G,P12);
C1=Circle3pts3D("C1",P11,P14,P12);
Symc4=Symmetry("Symc4",G,P11);
N=PointOn("N",C1,1039);
C4=Circle3pts3D("C4",P11,P13,Symc4);
C5=Circle3pts3D("C5",P12,P13,Symc5);
Center1=Center("Center1",C1);
Center2=Center("Center2",C5);
Center3=Center("Center3",C4);
Quad=Quadric("Quad",P11,P12,N,Symc4,Symc5);
P15=Point("P15","[(G[0]+N[0])/2,(G[1]+N[1])/2,G[2]+sqrt(3)*r/2]","1");
R=PointOn("R",C4,1136);
E4=ExpressionOn("E4","g(N)= aNA^2+bNB^2+cNC^2 = ","","","a*d(N,A)^2+b*d(N,B)^2+c*d(N,C)^2",P20,[20,-30]);
C2=Circle3pts3D("C2",N,P15,P13);
E8=ExpressionOn("E8","g(R) = aRA^2+bRB^2+cRC^2 = ","","","a*d(R,A)^2+b*d(R,B)^2+c*d(R,C)^2",P20,[20,30]);
E11=Expression("E11","","","","Quad.foci()","0.8008714453398192","-0.1973161531996656");
Center4=Center("Center4",C2);
P=PointOn("P",C2,435);
P81=Point("P81","E11[1]","0");
P71=Point("P71","E11[0]","0");
P17=Point("P17","[G[0]+G[1]-P[1],G[1]+G[0]-P[0],P[2]]","1");
P16=Point("P16","[2*G[0]-P[0],2*G[1]-P[1],P[2]]","1");
L1=Line("L1",P71,P81);
E6=ExpressionOn("E6","g(P) = aPA^2+bPB^2+cPC^2 = ","","","a*d(P,A)^2+b*d(P,B)^2+c*d(P,C)^2",P20,[20,-10]);
P18=OrderedIntersection("P18",L1,Quad,1);
C3=Circle3pts3D("C3",P16,P17,P);
Q=PointOn("Q",C3,1121);
Symc7=Symmetry("Symc7",G,P18);
Center5=Center("Center5",C3);
C6=Circle("C6",G,P18);
E7=ExpressionOn("E7","g(Q) = aQA^2+bQB^2+cQC^2 = ","","","a*d(Q,A)^2+b*d(Q,B)^2+c*d(Q,C)^2",P20,[20,10]);
Par1=Parallel("Par1",L1,Center5);


// Styles :
STL(O,"c:#966400;s:5;sn:true;f:17;sp:1;np:0.4353532751523024;fl:true");
STL(P4,"c:#0000b2;h:1;s:5;f:17");
STL(P3,"c:#0000b2;h:1;s:5;f:17");
STL(P19,"c:#0000b2;h:1;s:5;f:17");
STL(P5,"c:#0000b2;h:1;s:5;f:17");
STL(E15,"c:#cf0928;s:7;f:12;p:-1;cL:200;cPT:YzojNzgwMDEzO3M6MTA7ZjoxNw==");
STL(E14,"c:#cf0928;s:7;f:12;p:-1;cL:200;cPT:YzojNzgwMDEzO3M6MTA7ZjoxNw==");
STL(E13,"c:#4633db;s:7;f:14;p:-1;cL:200;cPT:YzojNzgwMDEzO3M6MTA7ZjoxNw==");
STL(E12,"c:#4633db;s:7;f:14;p:-1;cL:200;cPT:YzojNzgwMDEzO3M6MTA7ZjoxNw==");
STL(E10,"c:#007c7c;s:7;f:15;p:-1;cL:200;cPT:YzojNzgwMDEzO3M6MTA7ZjoxNw==");
STL(E9,"c:#007c7c;s:7;f:15;p:-1;cL:200;cPT:YzojNzgwMDEzO3M6MTA7ZjoxNw==");
STL(P20,"c:#0000b2;s:5;f:17;sp:1;fl:true");
STL(E5,"c:#e425df;s:5;f:16;p:-1;cL:200;cPT:YzojNzgwMDEzO3M6NTtmOjE3");
STL(P1,"c:#0000b2;s:5;f:17;sp:1;fl:true");
STL(X,"c:#0000b2;h:1;o:1;s:5;sn:true;f:17");
STL(P6,"c:#0000b2;h:1;s:5;f:17");
STL(Z,"c:#0000b2;h:1;o:1;s:5;sn:true;f:17");
STL(Y,"c:#0000b2;h:1;o:1;s:5;sn:true;f:17");
STL(E16,"c:#cf0928;s:7;f:12;p:-1;cL:200;cPT:YzojNzgwMDEzO3M6MTA7ZjoxNw==");
STL(P2,"c:#0000b2;h:1;s:5;f:17");
STL(E17,"c:#760012;s:7;f:20;p:-1;cL:200;cPT:YzojNzgwMDEzO3M6MTA7ZjozMA==");
STL(k,"c:#747c0c;s:5;sn:true;f:14;p:4;cL:200;cPT:YzojNzgwMDEzO3M6ODtmOjE3");
STL(S21,"c:#117dad;h:1;s:1;f:24");
STL(S11,"c:#117dad;h:1;s:1;f:24");
STL(b,"c:#27471a;s:5;sn:true;f:14;p:4;cL:180;cPT:YzojNzgwMDEzO3M6ODtmOjE3");
STL(S31,"c:#117dad;h:1;s:1;f:24");
STL(Poly1,"c:#966400;o:0.2;s:1;f:30");
STL(c,"c:#7a0256;s:5;sn:true;f:14;p:4;cL:160;cPT:YzojNzgwMDEzO3M6ODtmOjE3");
STL(S8,"c:#006633;h:1;s:1;f:24");
STL(a,"c:#687135;s:5;sn:true;f:14;p:4;cL:160;cPT:YzojNzgwMDEzO3M6ODtmOjE3");
STL(K,"c:#0000b2;o:1;s:5;sn:true;f:17;np:2.7609920575428215");
STL(I,"c:#0000b2;o:1;s:5;sn:true;f:17");
STL(M,"c:#354235;s:5;f:17;sp:1");
STL(J,"c:#0000b2;o:1;s:5;sn:true;f:17");
STL(angl25,"c:#006633;h:2;s:4;f:24;p:1");
STL(P8,"c:#0000b2;h:1;s:5;f:17");
STL(P9,"c:#0000b2;h:1;s:5;f:17");
STL(S104,"c:#4633db;s:1;f:24;dh:true");
STL(angl23,"c:#006633;h:2;s:4;f:24;p:1");
STL(angl24,"c:#006633;h:2;s:4;f:24;p:1");
STL(E1,"c:#00463a;h:1;s:5;f:14;p:4;cL:200;cPT:YzojMDAwMGIyO2g6MTtzOjU7ZjoxNw==");
STL(S103,"c:#0000b2;s:1;f:24");
STL(P7,"c:#0000b2;h:1;s:5;f:17");
STL(S7,"c:#3f4c45;s:1;f:24;dh:true");
STL(S105,"c:#4633db;s:1;f:24");
STL(Poly2,"c:#006633;h:1;o:0.2;s:1;f:30");
STL(L,"c:#0000b2;o:1;s:5;sn:true;f:17");
STL(Poly3,"c:#006633;h:1;o:0.2;s:1;f:30");
STL(angl1,"c:#006633;h:2;s:4;f:24;p:1");
STL(angl12,"c:#006633;h:2;s:4;f:24;p:1");
STL(S101,"c:#4633db;s:1;f:24");
STL(angl22,"c:#006633;h:2;s:4;f:24;p:1");
STL(S102,"c:#4633db;s:1;f:24");
STL(angl13,"c:#006633;h:2;s:4;f:24;p:1");
STL(S10,"c:#4633db;s:1;f:24");
STL(angl15,"c:#006633;h:2;s:4;f:24;p:1");
STL(angl2,"c:#006633;h:2;s:4;f:24;p:1");
STL(angl21,"c:#006633;h:2;s:4;f:24;p:1");
STL(angl11,"c:#006633;h:2;s:4;f:24;p:1");
STL(Poly5,"c:#006633;h:1;o:0.2;s:1;f:30");
STL(angl14,"c:#006633;h:2;s:4;f:24;p:1");
STL(Poly4,"c:#006633;h:1;o:0.2;s:1;f:30");
STL(A,"c:#cf0928;o:1;s:5;sn:true;f:17");
STL(E34,"c:#780013;h:2;s:5;f:14;p:4;cL:200;cPT:YzojNzgwMDEzO2g6MjtzOjU7ZjoxNw==");
STL(E32,"c:#780013;h:2;s:5;f:14;p:4;cL:200;cPT:YzojNzgwMDEzO2g6MjtzOjU7ZjoxNw==");
STL(C,"c:#cf0928;o:1;s:5;sn:true;f:17");
STL(E35,"c:#780013;h:2;s:5;f:14;p:4;cL:200;cPT:YzojNzgwMDEzO2g6MjtzOjU7ZjoxNw==");
STL(E31,"c:#780013;h:2;s:5;f:14;p:4;cL:200;cPT:YzojNzgwMDEzO2g6MjtzOjU7ZjoxNw==");
STL(E33,"c:#780013;h:2;s:5;f:14;p:4;cL:200;cPT:YzojNzgwMDEzO2g6MjtzOjU7ZjoxNw==");
STL(E3,"c:#780013;h:2;s:5;f:14;p:4;cL:200;cPT:YzojNzgwMDEzO2g6MjtzOjU7ZjoxNw==");
STL(B,"c:#cf0928;o:1;s:5;sn:true;f:17");
STL(G,"c:#006633;s:5;sn:true;f:17");
STL(S1,"c:#3a1a39;h:1;s:2;f:24");
STL(S2,"c:#3a1a39;h:1;s:2;f:24");
STL(P10,"c:#0000b2;h:1;s:5;f:17");
STL(Symc2,"c:#0000b2;h:1;s:5;f:17");
STL(CdG,"c:#761105;h:1;s:7;sn:true;f:14;p:4;cL:200;cPT:YzojNzgwMDEzO2g6MTtzOjU7ZjoxNw==");
STL(Symc6,"c:#0000b2;h:1;s:5;f:17");
STL(Symc3,"c:#0000b2;h:1;s:5;f:17");
STL(gG,"c:#760012;s:7;sn:true;f:14;p:4;cL:200;cPT:YzojNzgwMDEzO3M6NTtmOjE3");
STL(Symc1,"c:#0000b2;h:1;s:5;f:17");
STL(r,"c:#760012;s:7;sn:true;f:14;p:4;cL:200;cPT:YzojNzgwMDEzO3M6NTtmOjE3");
STL(Poly6,"c:#006633;o:0.2;s:1;f:30");
STL(E2,"c:#1a245a;h:1;s:7;f:14;p:4;cL:200;cPT:YzojNzgwMDEzO2g6MTtzOjU7ZjoxNw==");
STL(P12,"c:#966400;s:2;f:17");
STL(P13,"c:#966400;s:2;f:17");
STL(P14,"c:#0000b2;h:1;s:5;f:17");
STL(P11,"c:#966400;s:2;f:17");
STL(Symc5,"c:#0000b2;h:1;s:5;f:17");
STL(S3,"c:#966400;s:1;f:24;dh:true");
STL(S5,"c:#966400;s:1;f:24;dh:true");
STL(S4,"c:#966400;s:1;f:24;dh:true");
STL(C1,"c:#cc66cc;s:2;f:30;p:0");
STL(Symc4,"c:#0000b2;h:1;s:5;f:17");
STL(N,"c:#ea15e4;o:1;s:5;sn:true;f:17");
STL(C4,"c:#966400;s:1;f:30;p:0;dh:true");
STL(C5,"c:#966400;s:1;f:30;p:0;dh:true");
STL(Center1,"c:#0000b2;h:1;s:5;f:17");
STL(Center2,"c:#0000b2;h:1;s:5;f:17");
STL(Center3,"c:#0000b2;h:1;s:5;f:17");
STL(Quad,"c:#00adff;h:1;s:1;f:30;p:500");
STL(P15,"c:#0000b2;h:1;s:5;f:17");
STL(R,"c:#966400;o:1;s:5;sn:true;f:17");
STL(E4,"c:#ea15e4;s:7;f:14;p:4;cL:200;cPT:YzojNzgwMDEzO3M6NTtmOjE3");
STL(C2,"c:#2c69cf;s:2;f:30;p:0");
STL(E8,"c:#966400;s:7;f:14;p:4;cL:200;cPT:YzojNzgwMDEzO3M6NTtmOjE3");
STL(E11,"c:#780013;h:2;s:7;f:14;p:4;cL:200;cPT:YzojNzgwMDEzO2g6MjtzOjU7ZjoxNw==");
STL(Center4,"c:#0000b2;h:1;s:5;f:17");
STL(P,"c:#2c69cf;o:1;s:5;sn:true;f:17");
STL(P81,"c:#0000b2;h:1;s:5;f:17");
STL(P71,"c:#0000b2;h:1;s:5;f:17");
STL(P17,"c:#0000b2;h:1;s:5;f:17");
STL(P16,"c:#0000b2;h:1;s:5;f:17");
STL(L1,"c:#780013;h:1;s:1;f:30;p:0");
STL(E6,"c:#2c69cf;s:7;f:14;p:4;cL:200;cPT:YzojNzgwMDEzO3M6NTtmOjE3");
STL(P18,"c:#0000b2;h:1;s:5;f:17");
STL(C3,"c:#39aa44;s:2;f:30;p:0");
STL(Q,"c:#39aa44;o:1;s:5;sn:true;f:17");
STL(Symc7,"c:#0000b2;h:1;s:5;f:17");
STL(Center5,"c:#0000b2;h:1;s:5;f:17");
STL(C6,"c:#cc66cc;s:1;f:30;p:0");
STL(E7,"c:#39aa44;s:7;f:14;p:4;cL:200;cPT:YzojNzgwMDEzO3M6NTtmOjE3");
STL(Par1,"c:#780013;h:1;s:1;f:30;p:0");
SetCoordsStyle("3Dmode:true;isAxis:false;isGrid:true;isOx:true;isOy:true;isLockOx:false;isLockOy:false;centerZoom:true;color:#111111;fontSize:18;axisWidth:1;gridWidth:0.1");
SetGeneralStyle("background-color:#ffffff");