input geometriesyr16;

typerepre:="persp";

figureespace(-5u,-5u,5u,5u);
Initialisation(10,0,10,30);
trace cercles((0,0,0),(0,0,2),(0,0,0),(0,1,0),(0,0,1));
path CL;
CL=cercles((0,0,0),(0,2,0),(0,0,0),(0,1,0),(1,0,0));
trace subpath(0,length CL/2) of CL;
trace subpath(length CL/2,length CL) of CL dashed evenly;
color M,M';
M=(0,2*cosd(35),2*sind(35));
M'=(-1,0,bluepart(M));
color Cent;
Cent=(0,0,bluepart(M));
path Sect;
Sect=cercles(Cent,M,Cent,M,M');
remplis Sect withcolor 1.1*gris;
trace subpath(0,length Sect/2) of Sect dashed evenly;
trace subpath(length Sect/2,length Sect) of Sect;
trace polygone(Cent,M,(0,0,0)) dashed evenly;
trace codeperp((0,0,0),Cent,M,5);
marque_p:="plein";
pointe(M,(0,0,0),Cent);
marque_p:="non";
label.llft(btex $O$ etex,Projette((0,0,0)));
label.top(btex $I$ etex,Projette(Cent));
label.urt(btex $M$ etex,Projette(M));
finespace;

figureespace(-5u,-5u,5u,5u);
Initialisation(10,0,10,30);
trace cercles((0,0,0),(0,0,2),(0,0,0),(0,1,0),(0,0,1));
path CL;
color M,M';
color Cent;
Cent=1/2[(0,0,0),(0,2*cosd(45),2*sind(45))];
M=(0,2*cosd(-15),2*sind(-15));
M'=(-1,greenpart(Cent),bluepart(Cent));
path Sect;
Sect=cercles(Cent,M,Cent,M,M');
remplis Sect withcolor 1.1*gris;
trace subpath(0,length Sect/2) of Sect dashed evenly;
trace subpath(length Sect/2,length Sect) of Sect;
CL=cercles((0,0,0),(0,2,0),(0,0,0),(0,1,0),(1,0,0));
trace subpath(0,length CL/2) of CL;
trace subpath(length CL/2,length CL) of CL dashed evenly;
trace polygone(Cent,M,(0,0,0)) dashed evenly;
trace codeperp((0,0,0),Cent,M,5);
marque_p:="plein";
pointe(M,(0,0,0),Cent);
marque_p:="non";
label.llft(btex $O$ etex,Projette((0,0,0)));
label.top(btex $I$ etex,Projette(Cent));
label.lrt(btex $M$ etex,Projette(M));
finespace;

figureespace(-5u,-5u,5u,5u);
Initialisation(10,0,10,30);
trace cercles((0,0,0),(0,0,2),(0,0,0),(0,1,0),(0,0,1));
path CL;
color M,M';
color Cent;
M=(0,2*cosd(-130),2*sind(-130));
Cent=ProjectionsurPlan(M,(0,0,0),(0,2*cosd(120),2*sind(120)),(1,0,0));
M'=(-1,greenpart(Cent),bluepart(Cent));
path Sect;
Sect=cercles(Cent,M,Cent,M,M');
remplis Sect withcolor 1.1*gris;
trace subpath(0,length Sect/2) of Sect dashed evenly;
trace subpath(length Sect/2,length Sect) of Sect;
CL=cercles((0,0,0),(0,2,0),(0,0,0),(0,1,0),(1,0,0));
trace subpath(0,length CL/2) of CL;
trace subpath(length CL/2,length CL) of CL dashed evenly;
trace polygone(Cent,M,(0,0,0)) dashed evenly;
trace codeperp((0,0,0),Cent,M,5);
marque_p:="plein";
pointe(M,(0,0,0),Cent);
marque_p:="non";
label.top(btex $O$ etex,Projette((0,0,0)));
label.bot(btex $I$ etex,Projette(Cent));
label.llft(btex $M$ etex,Projette(M));
finespace;

figureespace(-5u,-5u,5u,5u);
Initialisation(10,0,10,30);
trace cercles((0,0,0),(0,0,2),(0,0,0),(0,1,0),(0,0,1));
path CL;
color M,M';
color Cent;
M=(0,2*cosd(100),2*sind(100));
Cent=ProjectionsurPlan(M,(0,0,0),(0,2*cosd(150),2*sind(150)),(1,0,0));
M'=(-1,greenpart(Cent),bluepart(Cent));
path Sect;
Sect=cercles(Cent,M,Cent,M,M');
remplis Sect withcolor 1.1*gris;
trace subpath(0,length Sect/2) of Sect dashed evenly;
trace subpath(length Sect/2,length Sect) of Sect;
CL=cercles((0,0,0),(0,2,0),(0,0,0),(0,1,0),(1,0,0));
trace subpath(0,length CL/2) of CL;
trace subpath(length CL/2,length CL) of CL dashed evenly;
trace polygone(Cent,M,(0,0,0)) dashed evenly;
trace codeperp((0,0,0),Cent,M,5);
marque_p:="plein";
pointe(M,(0,0,0),Cent);
marque_p:="non";
label.bot(btex $O$ etex,Projette((0,0,0)));
label.ulft(btex $I$ etex,Projette(Cent));
label.top(btex $M$ etex,Projette(M));
finespace;

figureespace(-5u,-5u,5u,5u);
Initialisation(10,0,10,30);
trace cercles((0,0,0),(0,0,2),(0,0,0),(0,1,0),(0,0,1));
path CL;
color M,M';
color Cent;
M=(0,2*cosd(-80),2*sind(-80));
Cent=ProjectionsurPlan(M,(0,0,0),(0,2*cosd(35),2*sind(35)),(1,0,0));
M'=(-1,greenpart(Cent),bluepart(Cent));
path Sect;
Sect=cercles(Cent,M,Cent,M,M');
remplis Sect withcolor 1.1*gris;
trace subpath(0,length Sect/2) of Sect dashed evenly;
trace subpath(length Sect/2,length Sect) of Sect;
CL=cercles((0,0,0),(0,2,0),(0,0,0),(0,1,0),(1,0,0));
trace subpath(0,length CL/2) of CL;
trace subpath(length CL/2,length CL) of CL dashed evenly;
trace polygone(Cent,M,(0,0,0)) dashed evenly;
trace codeperp((0,0,0),Cent,M,5);
marque_p:="plein";
pointe(M,(0,0,0),Cent);
marque_p:="non";
label.top(btex $O$ etex,Projette((0,0,0)));
label.ulft(btex $A$ etex,Projette(Cent));
label.bot(btex $B$ etex,Projette(M));
finespace;

figureespace(-5u,-5u,5u,5u);
Initialisation(10,0,10,30);
trace cercles((0,0,0),(0,0,2),(0,0,0),(0,1,0),(0,0,1));
path CL;
color M,M';
color Cent;
M=(0,2*cosd(130),2*sind(130));
Cent=ProjectionsurPlan(M,(0,0,0),(0,2*cosd(100),2*sind(100)),(1,0,0));
M'=(-1,greenpart(Cent),bluepart(Cent));
path Sect;
Sect=cercles(Cent,M,Cent,M,M');
remplis Sect withcolor 1.1*gris;
trace subpath(0,length Sect/2) of Sect dashed evenly;
trace subpath(length Sect/2,length Sect) of Sect;
CL=cercles((0,0,0),(0,2,0),(0,0,0),(0,1,0),(1,0,0));
trace subpath(0,length CL/2) of CL;
trace subpath(length CL/2,length CL) of CL dashed evenly;
trace polygone(Cent,M,(0,0,0)) dashed evenly;
trace codeperp((0,0,0),Cent,M,5);
marque_p:="plein";
pointe(M,(0,0,0),Cent);
marque_p:="non";
label.bot(btex $I$ etex,Projette((0,0,0)));
label.rt(btex $R$ etex,Projette(Cent));
label.ulft(btex $T$ etex,Projette(M));
finespace;

end