// Macros :
$macros={};
$macros["Cercles T1dtr 2P"]={
	name:"Cercles T1dtr 2P",
	parameters:["line","point","point"],
	exec:
	function (L1,A,B){
L2=Line("L2",A,B);
C1=Circle("C1",B,A);
C2=Circle("C2",A,B);
P3=OrderedIntersection("P3",L1,L2,0);
P4=OrderedIntersection("P4",C1,C2,1);
C3=Circle("C3",P4,A);
M1=MidPoint("M1",P3,P4);
C4=Circle("C4",M1,P4);
P5=OrderedIntersection("P5",C3,C4,0);
C5=Circle("C5",P3,P5);
P6=OrderedIntersection("P6",L1,C5,1);
P7=OrderedIntersection("P7",L1,C5,0);
C6=Circle3pts("C6",P6,B,A);
C7=Circle3pts("C7",P7,B,A);
return [C6,C7];
}};

$macros["ExoBergerTourne"]={
	name:"ExoBergerTourne",
	parameters:["point","point","point","point"],
	exec:
	function (M,B,C,I){
S2=Segment("S2",B,C);
S6=Segment("S6",C,I);
Syma1=Reflection("Syma1",S2,M);
Syma2=Reflection("Syma2",S6,M);
Par1=Parallel("Par1",S2,Syma1);
L2=Line("L2",M,Syma2);
C11=Circle("C11",Syma2,M);
C2=Circle("C2",M,Syma2);
P3=OrderedIntersection("P3",Par1,L2,0);
P4=OrderedIntersection("P4",C11,C2,1);
C3=Circle("C3",P4,M);
M11=MidPoint("M11",P3,P4);
C4=Circle("C4",M11,P4);
P5=OrderedIntersection("P5",C3,C4,0);
C5=Circle("C5",P3,P5);
P7=OrderedIntersection("P7",Par1,C5,0);
C7=Circle3pts("C7",P7,Syma2,M);
Center2=Center("Center2",C7);
Perp1=Perpendicular("Perp1",S2,Center2);
P1=OrderedIntersection("P1",S2,Perp1,0);
C6=Circle("C6",Center2,P1);
return [Center2,C6];
}};

// Coordinates System :
SetCoords(677.9834717290009,401.50641769219664,4.839513099987466);


// Geometry :
A=Point("A",-67.56536555916087,60.44129061102329);
B=Point("B",-121.08314609800698,18.908186795162024);
C=Point("C",-32.64449717667055,3.617392355491708);
ox=X_axis("ox");
oy=Y_axis("oy");
P2=Point("P2",-114.47091066463602,73.04586440588666);
S1=Segment("S1",A,B);
S2=Segment("S2",B,C);
S3=Segment("S3",C,A);
R1=AngleBisector("R1",A,B,C);
R2=AngleBisector("R2",C,A,B);
S21=Segment("S21",C,A);
S22=Segment("S22",A,B);
S23=Segment("S23",B,C);
S24=Segment("S24",C,A);
Par2=Parallel("Par2",ox,P2);
I=OrderedIntersection("I",R1,R2,0);
P8=PointOn("P8",Par2,60.714369530101635);
S4=Segment("S4",I,A);
S5=Segment("S5",I,B);
S6=Segment("S6",C,I);
S61=Segment("S61",A,I);
S62=Segment("S62",B,I);
S63=Segment("S63",C,I);
S64=Segment("S64",A,I);
Symc1=Symmetry("Symc1",P8,P2);
M=PointOn("M",S5,0.43039404758246164);
Symc2=Symmetry("Symc2",Symc1,P8);
Syma1=Reflection("Syma1",S2,M);
Syma2=Reflection("Syma2",S6,M);
Symc3=Symmetry("Symc3",Symc2,Symc1);
Par1=Parallel("Par1",S2,Syma1);
M1=MidPoint("M1",M,Syma1);
L2=Line("L2",M,Syma2);
C11=Circle("C11",Syma2,M);
C2=Circle("C2",M,Syma2);
Symc4=Symmetry("Symc4",Symc3,Symc2);
Cinit=Circle("Cinit",M,M1);
P3=OrderedIntersection("P3",Par1,L2,0);
P4=OrderedIntersection("P4",C11,C2,1);
Symc5=Symmetry("Symc5",Symc4,Symc3);
C3=Circle("C3",P4,M);
M11=MidPoint("M11",P3,P4);
S7=Segment("S7",Symc5,P2);
S8=Segment("S8",Symc5,P8);
S9=Segment("S9",Symc1,Symc5);
S10=Segment("S10",Symc2,Symc5);
S11=Segment("S11",Symc3,Symc5);
S12=Segment("S12",Symc4,Symc5);
C4=Circle("C4",M11,P4);
Ch=PointOn("Ch",S7,0.881960947266141);
P5=OrderedIntersection("P5",C3,C4,0);
Perp2=Perpendicular("Perp2",Par2,Ch);
C5=Circle("C5",P3,P5);
P9=OrderedIntersection("P9",S8,Perp2,0);
P10=OrderedIntersection("P10",S9,Perp2,0);
P15=OrderedIntersection("P15",S10,Perp2,0);
P16=OrderedIntersection("P16",S11,Perp2,0);
P17=OrderedIntersection("P17",S12,Perp2,0);
P6=OrderedIntersection("P6",Par1,C5,1);
P7=OrderedIntersection("P7",Par1,C5,0);
C7=Circle3pts("C7",P7,Syma2,M);
Center1=Center("Center1",C7);
Perp1=Perpendicular("Perp1",S2,Center1);
Syma11=Reflection("Syma11",S21,Center1);
Syma21=Reflection("Syma21",S61,Center1);
P1=OrderedIntersection("P1",S2,Perp1,0);
Par11=Parallel("Par11",S21,Syma11);
L21=Line("L21",Center1,Syma21);
C111=Circle("C111",Syma21,Center1);
C21=Circle("C21",Center1,Syma21);
Cb1=Circle("Cb1",Center1,P1);
P31=OrderedIntersection("P31",Par11,L21,0);
P41=OrderedIntersection("P41",C111,C21,1);
M2=MidPoint("M2",P1,P9);
C31=Circle("C31",P41,Center1);
M111=MidPoint("M111",P31,P41);
Symc6=Symmetry("Symc6",M2,P9);
C41=Circle("C41",M111,P41);
C1=Circle("C1",Center1,Symc6);
P51=OrderedIntersection("P51",C31,C41,0);
C51=Circle("C51",P31,P51);
P71=OrderedIntersection("P71",Par11,C51,0);
C71=Circle3pts("C71",P71,Syma21,Center1);
Center2=Center("Center2",C71);
Perp11=Perpendicular("Perp11",S21,Center2);
Syma12=Reflection("Syma12",S22,Center2);
Syma22=Reflection("Syma22",S62,Center2);
P11=OrderedIntersection("P11",S21,Perp11,0);
Par12=Parallel("Par12",S22,Syma12);
L22=Line("L22",Center2,Syma22);
C112=Circle("C112",Syma22,Center2);
C22=Circle("C22",Center2,Syma22);
Cb2=Circle("Cb2",Center2,P11);
P32=OrderedIntersection("P32",Par12,L22,0);
P42=OrderedIntersection("P42",C112,C22,1);
M3=MidPoint("M3",P11,P10);
C32=Circle("C32",P42,Center2);
M112=MidPoint("M112",P32,P42);
Symc7=Symmetry("Symc7",M3,P10);
C42=Circle("C42",M112,P42);
C6=Circle("C6",Center2,Symc7);
P52=OrderedIntersection("P52",C32,C42,0);
C52=Circle("C52",P32,P52);
P72=OrderedIntersection("P72",Par12,C52,0);
C72=Circle3pts("C72",P72,Syma22,Center2);
Center3=Center("Center3",C72);
Perp12=Perpendicular("Perp12",S22,Center3);
Syma13=Reflection("Syma13",S23,Center3);
Syma23=Reflection("Syma23",S63,Center3);
P12=OrderedIntersection("P12",S22,Perp12,0);
Par13=Parallel("Par13",S23,Syma13);
L23=Line("L23",Center3,Syma23);
C113=Circle("C113",Syma23,Center3);
C23=Circle("C23",Center3,Syma23);
Cb3=Circle("Cb3",Center3,P12);
P33=OrderedIntersection("P33",Par13,L23,0);
P43=OrderedIntersection("P43",C113,C23,1);
M4=MidPoint("M4",P12,P15);
C33=Circle("C33",P43,Center3);
M113=MidPoint("M113",P33,P43);
Symc8=Symmetry("Symc8",M4,P15);
C43=Circle("C43",M113,P43);
C8=Circle("C8",Center3,Symc8);
P53=OrderedIntersection("P53",C33,C43,0);
C53=Circle("C53",P33,P53);
P73=OrderedIntersection("P73",Par13,C53,0);
C73=Circle3pts("C73",P73,Syma23,Center3);
Center4=Center("Center4",C73);
Perp13=Perpendicular("Perp13",S23,Center4);
Syma14=Reflection("Syma14",S24,Center4);
Syma24=Reflection("Syma24",S64,Center4);
P13=OrderedIntersection("P13",S23,Perp13,0);
Par14=Parallel("Par14",S24,Syma14);
L24=Line("L24",Center4,Syma24);
C114=Circle("C114",Syma24,Center4);
C24=Circle("C24",Center4,Syma24);
Cb4=Circle("Cb4",Center4,P13);
P34=OrderedIntersection("P34",Par14,L24,0);
P44=OrderedIntersection("P44",C114,C24,1);
M5=MidPoint("M5",P13,P16);
C34=Circle("C34",P44,Center4);
M114=MidPoint("M114",P34,P44);
Symc9=Symmetry("Symc9",M5,P16);
C44=Circle("C44",M114,P44);
C9=Circle("C9",Center4,Symc9);
P54=OrderedIntersection("P54",C34,C44,0);
C54=Circle("C54",P34,P54);
P74=OrderedIntersection("P74",Par14,C54,0);
C74=Circle3pts("C74",P74,Syma24,Center4);
Center5=Center("Center5",C74);
Perp14=Perpendicular("Perp14",S24,Center5);
P14=OrderedIntersection("P14",S24,Perp14,0);
Cb5=Circle("Cb5",Center5,P14);
M6=MidPoint("M6",P14,P17);
Symc10=Symmetry("Symc10",M6,P17);
C10=Circle("C10",Center5,Symc10);


// Styles :
STL(A,"c:#0000b2;o:0.98;s:4.5;f:15");
STL(B,"c:#0000b2;o:0.98;s:4.5;f:15");
STL(C,"c:#0000b2;o:1;s:4.5;f:15");
STL(P2,"c:#0000b2;o:1;s:3;f:30");
STL(S1,"c:#0026ff;s:3.5;f:24");
STL(S2,"c:#0026ff;s:3.5;f:24");
STL(S3,"c:#0026ff;s:3.5;f:24");
STL(R1,"c:#0026ff;h:1;s:3.5;f:30;p:0");
STL(R2,"c:#0026ff;h:1;s:3.5;f:30;p:0");
STL(S21,"c:#0026ff;h:1;s:3.5;f:24");
STL(S22,"c:#0026ff;h:1;s:3.5;f:24");
STL(S23,"c:#0026ff;h:1;s:3.5;f:24");
STL(S24,"c:#0026ff;h:1;s:3.5;f:24");
STL(Par2,"c:#0026ff;h:1;s:3.5;f:30;p:0");
STL(I,"c:#0000b2;h:1;s:6;sn:true;f:15");
STL(P8,"c:#0000b2;h:1;s:6;f:30");
STL(S4,"c:#0026ff;h:1;s:3.5;f:24");
STL(S5,"c:#0026ff;h:1;s:3.5;f:24");
STL(S6,"c:#0026ff;h:1;s:3.5;f:24");
STL(S61,"c:#0026ff;h:1;s:3.5;f:24");
STL(S62,"c:#0026ff;h:1;s:3.5;f:24");
STL(S63,"c:#0026ff;h:1;s:3.5;f:24");
STL(S64,"c:#0026ff;h:1;s:3.5;f:24");
STL(Symc1,"c:#0000b2;h:1;s:6;f:30");
STL(M,"c:#b40000;o:1;s:4.5;f:15");
STL(Symc2,"c:#0000b2;h:1;s:6;f:30");
STL(Syma1,"c:#0000b2;h:1;s:6;f:15");
STL(Syma2,"c:#0000b2;h:1;s:6;f:15");
STL(Symc3,"c:#0000b2;h:1;s:6;f:30");
STL(Par1,"c:#0026ff;h:1;s:3.5;f:30;p:0");
STL(M1,"c:#0000b2;h:1;s:6;f:15");
STL(L2,"c:#0026ff;h:1;s:3.5;f:30;p:0");
STL(C11,"c:#cc66cc;h:1;s:1;f:30;p:0");
STL(C2,"c:#cc66cc;h:1;s:1;f:30;p:0");
STL(Symc4,"c:#0000b2;h:1;s:6;f:30");
STL(Cinit,"c:#b40000;s:2;sn:true;f:30;p:0");
STL(P3,"c:#0000b2;h:1;s:6;f:15");
STL(P4,"c:#0000b2;h:1;s:6;f:15");
STL(Symc5,"c:#0000b2;o:1;s:3;f:30");
STL(C3,"c:#cc66cc;h:1;s:1;f:30;p:0");
STL(M11,"c:#0000b2;h:1;s:6;f:15");
STL(S7,"c:#966400;s:1;f:24");
STL(S8,"c:#0026ff;h:1;s:3.5;f:24");
STL(S9,"c:#0026ff;h:1;s:3.5;f:24");
STL(S10,"c:#0026ff;h:1;s:3.5;f:24");
STL(S11,"c:#0026ff;h:1;s:3.5;f:24");
STL(S12,"c:#0026ff;h:1;s:3.5;f:24");
STL(C4,"c:#cc66cc;h:1;s:1;f:30;p:0");
STL(Ch,"c:#b40000;o:1;s:6;sn:true;f:16;np:1.467003986337854");
STL(P5,"c:#0000b2;h:1;s:6;f:15");
STL(Perp2,"c:#0026ff;h:1;s:3.5;f:30;p:0");
STL(C5,"c:#cc66cc;h:1;s:1;f:30;p:0");
STL(P9,"c:#0000b2;h:1;s:6;f:30");
STL(P10,"c:#0000b2;h:1;s:6;f:30");
STL(P15,"c:#0000b2;h:1;s:6;f:30");
STL(P16,"c:#0000b2;h:1;s:6;f:30");
STL(P17,"c:#0000b2;h:1;s:6;f:30");
STL(P6,"c:#0000b2;h:1;s:6;f:15");
STL(P7,"c:#0000b2;h:1;s:6;f:15");
STL(C7,"c:#cc66cc;h:1;s:1;f:30;p:0");
STL(Center1,"c:#0000b2;h:1;s:6;sn:true;f:15");
STL(Perp1,"c:#0026ff;h:1;s:3.5;f:30;p:0");
STL(Syma11,"c:#0000b2;h:1;s:6;f:15");
STL(Syma21,"c:#0000b2;h:1;s:6;f:15");
STL(P1,"c:#0000b2;h:1;s:6;sn:true;f:15;np:5.251282876140539");
STL(Par11,"c:#0026ff;h:1;s:3.5;f:30;p:0");
STL(L21,"c:#0026ff;h:1;s:3.5;f:30;p:0");
STL(C111,"c:#cc66cc;h:1;s:1;f:30;p:0");
STL(C21,"c:#cc66cc;h:1;s:1;f:30;p:0");
STL(Cb1,"c:#0000b2;h:1;s:2;sn:true;f:30;p:0");
STL(P31,"c:#0000b2;h:1;s:6;f:15");
STL(P41,"c:#0000b2;h:1;s:6;f:15");
STL(M2,"c:#0000b2;h:1;s:6;f:30");
STL(C31,"c:#cc66cc;h:1;s:1;f:30;p:0");
STL(M111,"c:#0000b2;h:1;s:6;f:15");
STL(Symc6,"c:#0000b2;h:1;s:6;f:30");
STL(C41,"c:#cc66cc;h:1;s:1;f:30;p:0");
STL(C1,"c:#0000b2;s:2;f:30;p:0");
STL(P51,"c:#0000b2;h:1;s:6;f:15");
STL(C51,"c:#cc66cc;h:1;s:1;f:30;p:0");
STL(P71,"c:#0000b2;h:1;s:6;f:15");
STL(C71,"c:#cc66cc;h:1;s:1;f:30;p:0");
STL(Center2,"c:#0000b2;h:1;s:6;sn:true;f:15;np:1.994620503739397");
STL(Perp11,"c:#0026ff;h:1;s:3.5;f:30;p:0");
STL(Syma12,"c:#0000b2;h:1;s:6;f:15");
STL(Syma22,"c:#0000b2;h:1;s:6;f:15");
STL(P11,"c:#0000b2;h:1;s:6;sn:true;f:15");
STL(Par12,"c:#0026ff;h:1;s:3.5;f:30;p:0");
STL(L22,"c:#0026ff;h:1;s:3.5;f:30;p:0");
STL(C112,"c:#cc66cc;h:1;s:1;f:30;p:0");
STL(C22,"c:#cc66cc;h:1;s:1;f:30;p:0");
STL(Cb2,"c:#13c413;h:1;s:3.5;sn:true;f:30;p:0");
STL(P32,"c:#0000b2;h:1;s:6;f:15");
STL(P42,"c:#0000b2;h:1;s:6;f:15");
STL(M3,"c:#0000b2;h:1;s:6;f:30");
STL(C32,"c:#cc66cc;h:1;s:1;f:30;p:0");
STL(M112,"c:#0000b2;h:1;s:6;f:15");
STL(Symc7,"c:#0000b2;h:1;s:6;f:30");
STL(C42,"c:#cc66cc;h:1;s:1;f:30;p:0");
STL(C6,"c:#00ff1c;s:2;f:30;p:0");
STL(P52,"c:#0000b2;h:1;s:6;f:15");
STL(C52,"c:#cc66cc;h:1;s:1;f:30;p:0");
STL(P72,"c:#0000b2;h:1;s:6;f:15");
STL(C72,"c:#cc66cc;h:1;s:1;f:30;p:0");
STL(Center3,"c:#0000b2;h:1;s:6;sn:true;f:15;np:1.81830400840759");
STL(Perp12,"c:#0026ff;h:1;s:3.5;f:30;p:0");
STL(Syma13,"c:#0000b2;h:1;s:6;f:15");
STL(Syma23,"c:#0000b2;h:1;s:6;f:15");
STL(P12,"c:#0000b2;h:1;s:6;sn:true;f:15;np:2.039748298466294");
STL(Par13,"c:#0026ff;h:1;s:3.5;f:30;p:0");
STL(L23,"c:#0026ff;h:1;s:3.5;f:30;p:0");
STL(C113,"c:#cc66cc;h:1;s:1;f:30;p:0");
STL(C23,"c:#cc66cc;h:1;s:1;f:30;p:0");
STL(Cb3,"c:#755310;h:1;s:2;sn:true;f:30;p:0");
STL(P33,"c:#0000b2;h:1;s:6;f:15");
STL(P43,"c:#0000b2;h:1;s:6;f:15");
STL(M4,"c:#0000b2;h:1;s:6;f:30");
STL(C33,"c:#cc66cc;h:1;s:1;f:30;p:0");
STL(M113,"c:#0000b2;h:1;s:6;f:15");
STL(Symc8,"c:#0000b2;h:1;s:6;f:30");
STL(C43,"c:#cc66cc;h:1;s:1;f:30;p:0");
STL(C8,"c:#966400;s:2;f:30;p:0");
STL(P53,"c:#0000b2;h:1;s:6;f:15");
STL(C53,"c:#cc66cc;h:1;s:1;f:30;p:0");
STL(P73,"c:#0000b2;h:1;s:6;f:15");
STL(C73,"c:#cc66cc;h:1;s:1;f:30;p:0");
STL(Center4,"c:#0000b2;h:1;s:6;sn:true;f:15");
STL(Perp13,"c:#0026ff;h:1;s:3.5;f:30;p:0");
STL(Syma14,"c:#0000b2;h:1;s:6;f:15");
STL(Syma24,"c:#0000b2;h:1;s:6;f:15");
STL(P13,"c:#0000b2;h:1;s:6;sn:true;f:15;np:5.313077867324984");
STL(Par14,"c:#0026ff;h:1;s:3.5;f:30;p:0");
STL(L24,"c:#0026ff;h:1;s:3.5;f:30;p:0");
STL(C114,"c:#cc66cc;h:1;s:1;f:30;p:0");
STL(C24,"c:#cc66cc;h:1;s:1;f:30;p:0");
STL(Cb4,"c:#007c7c;h:1;s:2;sn:true;f:30;p:0");
STL(P34,"c:#0000b2;h:1;s:6;f:15");
STL(P44,"c:#0000b2;h:1;s:6;f:15");
STL(M5,"c:#0000b2;h:1;s:6;f:30");
STL(C34,"c:#cc66cc;h:1;s:1;f:30;p:0");
STL(M114,"c:#0000b2;h:1;s:6;f:15");
STL(Symc9,"c:#0000b2;h:1;s:6;f:30");
STL(C44,"c:#cc66cc;h:1;s:1;f:30;p:0");
STL(C9,"c:#0044ff;s:2;f:30;p:0");
STL(P54,"c:#0000b2;h:1;s:6;f:15");
STL(C54,"c:#cc66cc;h:1;s:1;f:30;p:0");
STL(P74,"c:#0000b2;h:1;s:6;f:15");
STL(C74,"c:#cc66cc;h:1;s:1;f:30;p:0");
STL(Center5,"c:#0000b2;h:1;s:6;sn:true;f:15");
STL(Perp14,"c:#0026ff;h:1;s:3.5;f:30;p:0");
STL(P14,"c:#0000b2;h:1;s:6;sn:true;f:15");
STL(Cb5,"c:#f731f7;h:1;s:2;sn:true;f:30;p:0");
STL(M6,"c:#0000b2;h:1;s:6;f:30");
STL(Symc10,"c:#0000b2;h:1;s:6;f:30");
STL(C10,"c:#ef11ef;s:2;f:30;p:0");
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// Texts :
Text("<b>Théorème des six cercles</b>.<br><br>Un premier cercle est tangent à deux côtés d'un triangle.<br>En tournant dans un sens (<b>déplacer Ch</b>),on poursuit par<br> un cercle tangent au précédent et à deux côtés du triangle.<br>Alors le 6° cercle est tangent au 1° (ou le 7° est confondu au 1°)<br><br><b>Cas 1</b> : confondus deux à deux (Malffati).<br><b>Cas 2</b> : trois cercles confondus avec le cercle inscrit.",40,435,487,184);