%%% % Thales %%% \newcount\ppcm% \newcommand\PPCM[2]{% \PGCD{#1}{#2}% \ppcm=\numexpr#1*#2/\pgcd\relax% }% \setKVdefault[ClesThales]{Calcul=true,Droites=false,Propor=false,Segment=false,Figure=false,FigureSeule=false,Figurecroisee=false,FigurecroiseeSeule=false,Angle=0,Precision=2,Entier=false,Unite=cm,Reciproque=false,Produit=false,ChoixCalcul=0,Simplification,Redaction=false,Remediation=false,Echelle=1cm,Perso=false,CalculsPerso=false,IntroCalculs,CouleursNum=false,CouleursDen=false,ModeleCouleur=5} \defKV[ClesThales]{CouleurNum=\setKV[ClesThales]{CouleursNum}} \defKV[ClesThales]{CouleurDen=\setKV[ClesThales]{CouleursDen}} \DeclareSIUnit{\PfCThalesUnit}{\useKV[ClesThales]{Unite}}% %On d\'efinit la figure \`a utiliser \def\MPFigThales#1#2#3#4#5#6{ % #1 Premier sommet % #2 Deuxi\`eme sommet % #3 Troisi\`eme sommet % #4 point sur le segment #1#2 % #5 point sur le segment #1#3 % #6 angle de rotation \ifluatex % \mplibcodeinherit{enable} \mplibforcehmode \begin{mplibcode} defaultcolormodel := \useKV[ClesThales]{ModeleCouleur}; u:=\useKV[ClesThales]{Echelle}; boolean CouleursNum,CouleursDen; CouleursNum=\useKV[ClesThales]{CouleursNum}; CouleursDen=\useKV[ClesThales]{CouleursDen}; color CouleurNum,CouleurDen; if CouleursNum: CouleurNum=\useKV[ClesThales]{CouleurNum} else: CouleurNum=black fi; if CouleursDen: CouleurDen=\useKV[ClesThales]{CouleurDen} else: CouleurDen=black fi; pair A,B,C,M,N,O;% %On place les points A,B,C sur le cercle de mani\`ere \`a faciliter la rotation de la figure A=u*(1,1); B-A=u*(4,0); C=(A--2[A,B rotatedabout(A,45)]) intersectionpoint (B--2[B,A rotatedabout(B,-60)]); % On d\'efinit le centre du cercle circonscrit O - .5[A,B] = whatever * (B-A) rotated 90; O - .5[B,C] = whatever * (C-B) rotated 90; % On tourne pour \'eventuellement moins de lassitude :) A:=A rotatedabout(O,#6); B:=B rotatedabout(O,#6); C:=C rotatedabout(O,#6); % on dessine \`a main lev\'ee :) path cotes[]; cotes1=A{dir(angle(B-A)+5)}..B{dir(angle(B-A)+5)}; cotes2=B{dir(angle(C-B)+5)}..C{dir(angle(C-B)+5)}; cotes3=C{dir(angle(A-C)+5)}..A{dir(angle(A-C)+5)}; M=point(0.4*length cotes1) of cotes1; N=point(0.6*length cotes3) of cotes3; cotes4=1.5[N,M]{dir(angle(N-M)+5)}..1.5[M,N]{dir(angle(N-M)+5)}; path triangle; triangle=cotes1--cotes2--cotes3--cycle; draw triangle; draw cotes4; if CouleursDen: draw triangle dashed evenly withpen pencircle scaled 1.5 withcolor CouleurDen; fi; if CouleursNum: draw (cotes1 cutafter cotes4) dashed dashpattern(off 3 on 3) withpen pencircle scaled 1.5 withcolor CouleurNum; draw (cotes4 cutbefore cotes1 cutafter cotes3) dashed dashpattern(off 3 on 3) withpen pencircle scaled 1.5 withcolor CouleurNum; draw (cotes3 cutbefore cotes4) dashed dashpattern(off 3 on 3) withpen pencircle scaled 1.5 withcolor CouleurNum; fi; %on labelise label(btex #1 etex,1.15[O,A]); label(btex #2 etex,1.15[O,B]); label(btex #3 etex,1.15[O,C]); label(btex #4 etex,1.1[C,M]); label(btex #5 etex,1.1[B,N]); fill (fullcircle scaled 0.75mm) shifted (cotes1 intersectionpoint cotes4); fill (fullcircle scaled 0.75mm) shifted (cotes3 intersectionpoint cotes4); pair I,J,K; I=1/2[M,N]; J=1/2[B,C]; K=1/2[I,J]; path cd; cd=(fullcircle scaled 6mm) shifted K; drawoptions(withcolor 0.75*white); drawarrow reverse((I{dir(210+angle(I-J))}..{dir(150+angle(I-J))}K) cutafter cd); drawarrow reverse((J{dir(210+angle(J-I))}..{dir(150+angle(J-I))}K) cutafter cd); draw cd; label(btex $//$ etex ,K); drawoptions(); \end{mplibcode} % \mplibcodeinherit{disable} \else \begin{mpost}[mpsettings={u:=\useKV[ClesThales]{Echelle};boolean CouleursNum,CouleursDen; CouleursNum=\useKV[ClesThales]{CouleursNum}; CouleursDen=\useKV[ClesThales]{CouleursDen}; color CouleurNum,CouleurDen; if CouleursNum: CouleurNum=\useKV[ClesThales]{CouleurNum} else: CouleurNum=black fi; if CouleursDen: CouleurDen=\useKV[ClesThales]{CouleurDen} else: CouleurDen=black fi;}] pair A,B,C,M,N,O;% %On place les points A,B,C sur le cercle de mani\`ere \`a faciliter la rotation de la figure A=u*(1,1); B-A=u*(4,0); C=(A--2[A,B rotatedabout(A,45)]) intersectionpoint (B--2[B,A rotatedabout(B,-60)]); % On d\'efinit le centre du cercle circonscrit O - .5[A,B] = whatever * (B-A) rotated 90; O - .5[B,C] = whatever * (C-B) rotated 90; % On tourne pour \'eventuellement moins de lassitude :) A:=A rotatedabout(O,#6); B:=B rotatedabout(O,#6); C:=C rotatedabout(O,#6); % on dessine \`a main lev\'ee :) path cotes[]; cotes1=A{dir(angle(B-A)+5)}..B{dir(angle(B-A)+5)}; cotes2=B{dir(angle(C-B)+5)}..C{dir(angle(C-B)+5)}; cotes3=C{dir(angle(A-C)+5)}..A{dir(angle(A-C)+5)}; M=point(0.4*length cotes1) of cotes1; N=point(0.6*length cotes3) of cotes3; cotes4=1.5[N,M]{dir(angle(N-M)+5)}..1.5[M,N]{dir(angle(N-M)+5)}; path triangle; triangle=cotes1--cotes2--cotes3--cycle; draw triangle; draw cotes4; if CouleursDen: draw triangle dashed evenly withpen pencircle scaled 1.5 withcolor CouleurDen; fi; if CouleursNum: draw (cotes1 cutafter cotes4) dashed dashpattern(off 3 on 3) withpen pencircle scaled 1.5 withcolor CouleurNum; draw (cotes4 cutbefore cotes1 cutafter cotes3) dashed dashpattern(off 3 on 3) withpen pencircle scaled 1.5 withcolor CouleurNum; draw (cotes3 cutbefore cotes4) dashed dashpattern(off 3 on 3) withpen pencircle scaled 1.5 withcolor CouleurNum; fi; %on labelise label(btex #1 etex,1.15[O,A]); label(btex #2 etex,1.15[O,B]); label(btex #3 etex,1.15[O,C]); label(btex #4 etex,1.1[C,M]); label(btex #5 etex,1.1[B,N]); fill (fullcircle scaled 0.75mm) shifted (cotes1 intersectionpoint cotes4); fill (fullcircle scaled 0.75mm) shifted (cotes3 intersectionpoint cotes4); pair I,J,K; I=1/2[M,N]; J=1/2[B,C]; K=1/2[I,J]; path cd; cd=(fullcircle scaled 6mm) shifted K; drawoptions(withcolor 0.75*white); drawarrow reverse((I{dir(210+angle(I-J))}..{dir(150+angle(I-J))}K) cutafter cd); drawarrow reverse((J{dir(210+angle(J-I))}..{dir(150+angle(J-I))}K) cutafter cd); draw cd; label(btex $//$ etex ,K); drawoptions(); \end{mpost} \fi } %On d\'efinit la figure \`a utiliser \def\MPFigReciThales#1#2#3#4#5#6{ % #1 Premier sommet % #2 Deuxi\`eme sommet % #3 Troisi\`eme sommet % #4 point sur le segment #1#2 % #5 point sur le segment #1#3 \ifluatex % \mplibcodeinherit{enable} \mplibforcehmode \begin{mplibcode} defaultcolormodel := \useKV[ClesThales]{ModeleCouleur}; u:=\useKV[ClesThales]{Echelle}; pair A,B,C,M,N,O;% %On place les points A,B,C sur le cercle de mani\`ere \`a faciliter la rotation de la figure A=u*(1,1); B-A=u*(4,0); C=(A--2[A,B rotatedabout(A,45)]) intersectionpoint (B--2[B,A rotatedabout(B,-60)]); % On d\'efinit le centre du cercle circonscrit O - .5[A,B] = whatever * (B-A) rotated 90; O - .5[B,C] = whatever * (C-B) rotated 90; % On tourne pour \'eventuellement moins de lassitude :) A:=A rotatedabout(O,#6); B:=B rotatedabout(O,#6); C:=C rotatedabout(O,#6); % on dessine \`a main lev\'ee :) path cotes[]; cotes1=A{dir(angle(B-A)+5)}..B{dir(angle(B-A)+5)}; cotes2=B{dir(angle(C-B)+5)}..C{dir(angle(C-B)+5)}; cotes3=C{dir(angle(A-C)+5)}..A{dir(angle(A-C)+5)}; M=point(0.4*length cotes1) of cotes1; N=point(0.6*length cotes3) of cotes3; cotes4=1.5[N,M]{dir(angle(N-M)+5)}..1.5[M,N]{dir(angle(N-M)+5)}; path triangle; triangle=cotes1--cotes2--cotes3--cycle; draw triangle; draw cotes4; %on labelise label(btex #1 etex,1.15[O,A]); label(btex #2 etex,1.15[O,B]); label(btex #3 etex,1.15[O,C]); label(btex #4 etex,1.1[C,M]); label(btex #5 etex,1.1[B,N]); fill (fullcircle scaled 0.75mm) shifted (cotes1 intersectionpoint cotes4); fill (fullcircle scaled 0.75mm) shifted (cotes3 intersectionpoint cotes4); \end{mplibcode} % \mplibcodeinherit{disable} \else \begin{mpost}[mpsettings={u:=\useKV[ClesThales]{Echelle};}] pair A,B,C,M,N,O;% %On place les points A,B,C sur le cercle de mani\`ere \`a faciliter la rotation de la figure A=u*(1,1); B-A=u*(4,0); C=(A--2[A,B rotatedabout(A,45)]) intersectionpoint (B--2[B,A rotatedabout(B,-60)]); % On d\'efinit le centre du cercle circonscrit O - .5[A,B] = whatever * (B-A) rotated 90; O - .5[B,C] = whatever * (C-B) rotated 90; % On tourne pour \'eventuellement moins de lassitude :) A:=A rotatedabout(O,#6); B:=B rotatedabout(O,#6); C:=C rotatedabout(O,#6); % on dessine \`a main lev\'ee :) path cotes[]; cotes1=A{dir(angle(B-A)+5)}..B{dir(angle(B-A)+5)}; cotes2=B{dir(angle(C-B)+5)}..C{dir(angle(C-B)+5)}; cotes3=C{dir(angle(A-C)+5)}..A{dir(angle(A-C)+5)}; M=point(0.4*length cotes1) of cotes1; N=point(0.6*length cotes3) of cotes3; cotes4=1.5[N,M]{dir(angle(N-M)+5)}..1.5[M,N]{dir(angle(N-M)+5)}; path triangle; triangle=cotes1--cotes2--cotes3--cycle; draw triangle; draw cotes4; %on labelise label(btex #1 etex,1.15[O,A]); label(btex #2 etex,1.15[O,B]); label(btex #3 etex,1.15[O,C]); label(btex #4 etex,1.1[C,M]); label(btex #5 etex,1.1[B,N]); fill (fullcircle scaled 0.75mm) shifted (cotes1 intersectionpoint cotes4); fill (fullcircle scaled 0.75mm) shifted (cotes3 intersectionpoint cotes4); \end{mpost} \fi } %On d\'efinit la deuxi\`eme figure \`a utiliser \def\MPFigThalesCroisee#1#2#3#4#5#6{% % #1 Premier sommet % #2 Deuxi\`eme sommet % #3 Troisi\`eme sommet % #4 point sur la droite #1#2 % #5 point sur la droite #1#3 \ifluatex \mplibforcehmode % \mplibcodeinherit{enable} \begin{mplibcode} defaultcolormodel := \useKV[ClesThales]{ModeleCouleur}; u:=\useKV[ClesThales]{Echelle}; boolean CouleursNum,CouleursDen; CouleursNum=\useKV[ClesThales]{CouleursNum}; CouleursDen=\useKV[ClesThales]{CouleursDen}; color CouleurNum,CouleurDen; if CouleursNum: CouleurNum=\useKV[ClesThales]{CouleurNum} else: CouleurNum=black fi; if CouleursDen: CouleurDen=\useKV[ClesThales]{CouleurDen} else: CouleurDen=black fi; pair A,B,C,M,N,O;% O=(2.5u,2.5u); path cc; cc=(fullcircle scaled 3u) shifted O; %On place les points A,B,C sur le cercle de mani\`ere \`a faciliter la rotation de la figure A=point(0.1*length cc) of cc; B=A rotatedabout(O,130); C=(A--2[A,B rotatedabout(A,45)]) intersectionpoint (B--2[B,A rotatedabout(B,-60)]); % On tourne pour \'eventuellement moins de lassitude :) A:=A rotatedabout(O,#6); B:=B rotatedabout(O,#6); C:=C rotatedabout(O,#6); % on dessine \`a main lev\'ee :) M=1.4[B,A]; N=1.4[C,A]; path cotes[]; cotes1=A{dir(angle(B-A)+5)}..1.15[A,B]{dir(angle(B-A)+5)}; cotes2=1.15[C,B]{dir(angle(C-B)+5)}..1.15[B,C]{dir(angle(C-B)+5)}; cotes3=1.15[A,C]{dir(angle(A-C)+5)}..A{dir(angle(A-C)+5)}; cotes4=1.5[N,M]{dir(angle(N-M)+5)}..1.5[M,N]{dir(angle(N-M)+5)}; cotes5=A{dir(angle(M-A)+5)}..1.15[A,M]{dir(angle(M-A)+5)}; cotes6=A{dir(angle(N-A)+5)}..1.15[A,N]{dir(angle(N-A)+5)}; for k=1 upto 6: draw cotes[k]; endfor; if CouleursDen: drawoptions(dashed evenly withpen pencircle scaled 1.5 withcolor CouleurDen); draw (cotes[1] cutafter cotes[2]); draw (cotes[2] cutbefore cotes[1] cutafter cotes[3]); draw (cotes[3] cutbefore cotes[2]); drawoptions(); fi; if CouleursNum: drawoptions(dashed evenly withpen pencircle scaled 1.5 withcolor CouleurNum); draw (cotes[5] cutafter cotes[4]); draw (cotes[4] cutbefore cotes[5] cutafter cotes[6]); draw (cotes[6] cutafter cotes[4]); drawoptions(); fi; pair I; % On d\'efinit le centre du cercle inscrit \`a AMC (I-C) rotated ((angle(A-C)-angle(M-C))/2) shifted C=whatever[A,C]; (I-M) rotated ((angle(C-M)-angle(A-M))/2) shifted M=whatever[M,C]; %on labelise label(btex #1 etex,I); label(btex #2 etex,1.2[M,B]); label(btex #3 etex,1.2[N,C]); label(btex #4 etex,1.1[B,M]); label(btex #5 etex,1.1[C,N]); fill (fullcircle scaled 0.75mm) shifted (cotes5 intersectionpoint cotes4); fill (fullcircle scaled 0.75mm) shifted (cotes6 intersectionpoint cotes4); pair I,J,K; I=1.1[N,M]; J=1.1[B,C]; K=1/2[I,J]; path cd; cd=(fullcircle scaled 6mm) shifted K; drawoptions(withcolor 0.75*white); drawarrow reverse((I{dir(210+angle(I-J))}..{dir(150+angle(I-J))}K) cutafter cd); drawarrow reverse((J{dir(210+angle(J-I))}..{dir(150+angle(J-I))}K) cutafter cd); draw cd; label(btex $//$ etex ,K); drawoptions(); \end{mplibcode} % \mplibcodeinherit{disable} \else \begin{mpost}[mpsettings={u:=\useKV[ClesThales]{Echelle};boolean CouleursNum,CouleursDen; CouleursNum=\useKV[ClesThales]{CouleursNum}; CouleursDen=\useKV[ClesThales]{CouleursDen}; color CouleurNum,CouleurDen; if CouleursNum: CouleurNum=\useKV[ClesThales]{CouleurNum} else: CouleurNum=black fi; if CouleursDen: CouleurDen=\useKV[ClesThales]{CouleurDen} else: CouleurDen=black fi;}] pair A,B,C,M,N,O;% O=(2.5u,2.5u); path cc; cc=(fullcircle scaled 3u) shifted O; %On place les points A,B,C sur le cercle de mani\`ere \`a faciliter la rotation de la figure A=point(0.1*length cc) of cc; B=A rotatedabout(O,130); C=(A--2[A,B rotatedabout(A,45)]) intersectionpoint (B--2[B,A rotatedabout(B,-60)]); % On tourne pour \'eventuellement moins de lassitude :) A:=A rotatedabout(O,#6); B:=B rotatedabout(O,#6); C:=C rotatedabout(O,#6); % on dessine \`a main lev\'ee :) M=1.4[B,A]; N=1.4[C,A]; path cotes[]; cotes1=A{dir(angle(B-A)+5)}..1.15[A,B]{dir(angle(B-A)+5)}; cotes2=1.15[C,B]{dir(angle(C-B)+5)}..1.15[B,C]{dir(angle(C-B)+5)}; cotes3=1.15[A,C]{dir(angle(A-C)+5)}..A{dir(angle(A-C)+5)}; cotes4=1.5[N,M]{dir(angle(N-M)+5)}..1.5[M,N]{dir(angle(N-M)+5)}; cotes5=A{dir(angle(M-A)+5)}..1.15[A,M]{dir(angle(M-A)+5)}; cotes6=A{dir(angle(N-A)+5)}..1.15[A,N]{dir(angle(N-A)+5)}; for k=1 upto 6: draw cotes[k]; endfor; if CouleursDen: drawoptions(dashed evenly withpen pencircle scaled 1.5 withcolor CouleurDen); draw (cotes[1] cutafter cotes[2]); draw (cotes[2] cutbefore cotes[1] cutafter cotes[3]); draw (cotes[3] cutbefore cotes[2]); drawoptions(); fi; if CouleursNum: drawoptions(dashed evenly withpen pencircle scaled 1.5 withcolor CouleurNum); draw (cotes[5] cutafter cotes[4]); draw (cotes[4] cutbefore cotes[5] cutafter cotes[6]); draw (cotes[6] cutafter cotes[4]); drawoptions(); fi; pair I; % On d\'efinit le centre du cercle inscrit \`a AMC (I-C) rotated ((angle(A-C)-angle(M-C))/2) shifted C=whatever[A,C]; (I-M) rotated ((angle(C-M)-angle(A-M))/2) shifted M=whatever[M,C]; %on labelise label(btex #1 etex,I); label(btex #2 etex,1.2[M,B]); label(btex #3 etex,1.2[N,C]); label(btex #4 etex,1.1[B,M]); label(btex #5 etex,1.1[C,N]); fill (fullcircle scaled 0.75mm) shifted (cotes5 intersectionpoint cotes4); fill (fullcircle scaled 0.75mm) shifted (cotes6 intersectionpoint cotes4); pair I,J,K; I=1.1[N,M]; J=1.1[B,C]; K=1/2[I,J]; path cd; cd=(fullcircle scaled 6mm) shifted K; drawoptions(withcolor 0.75*white); drawarrow reverse((I{dir(210+angle(I-J))}..{dir(150+angle(I-J))}K) cutafter cd); drawarrow reverse((J{dir(210+angle(J-I))}..{dir(150+angle(J-I))}K) cutafter cd); draw cd; label(btex $//$ etex ,K); drawoptions(); \end{mpost} \fi } %On d\'efinit la deuxi\`eme figure \`a utiliser \def\MPFigReciThalesCroisee#1#2#3#4#5#6{% % #1 Premier sommet % #2 Deuxi\`eme sommet % #3 Troisi\`eme sommet % #4 point sur la droite #1#2 % #5 point sur la droite #1#3 \ifluatex \mplibforcehmode % \mplibcodeinherit{enable} \begin{mplibcode} defaultcolormodel := \useKV[ClesThales]{ModeleCouleur}; u:=\useKV[ClesThales]{Echelle}; pair A,B,C,M,N,O;% O=(2.5u,2.5u); path cc; cc=(fullcircle scaled 3u) shifted O; %On place les points A,B,C sur le cercle de mani\`ere \`a faciliter la rotation de la figure A=point(0.1*length cc) of cc; B=A rotatedabout(O,130); C=(A--2[A,B rotatedabout(A,45)]) intersectionpoint (B--2[B,A rotatedabout(B,-60)]); % On tourne pour \'eventuellement moins de lassitude :) A:=A rotatedabout(O,#6); B:=B rotatedabout(O,#6); C:=C rotatedabout(O,#6); % on dessine \`a main lev\'ee :) M=1.4[B,A]; N=1.4[C,A]; path cotes[]; cotes1=A{dir(angle(B-A)+5)}..1.15[A,B]{dir(angle(B-A)+5)}; cotes2=1.15[C,B]{dir(angle(C-B)+5)}..1.15[B,C]{dir(angle(C-B)+5)}; cotes3=1.15[A,C]{dir(angle(A-C)+5)}..A{dir(angle(A-C)+5)}; cotes4=1.5[N,M]{dir(angle(N-M)+5)}..1.5[M,N]{dir(angle(N-M)+5)}; cotes5=A{dir(angle(M-A)+5)}..1.15[A,M]{dir(angle(M-A)+5)}; cotes6=A{dir(angle(N-A)+5)}..1.15[A,N]{dir(angle(N-A)+5)}; for k=1 upto 6: draw cotes[k]; endfor; pair I; % On d\'efinit le centre du cercle inscrit \`a AMC (I-C) rotated ((angle(A-C)-angle(M-C))/2) shifted C=whatever[A,C]; (I-M) rotated ((angle(C-M)-angle(A-M))/2) shifted M=whatever[M,C]; %on labelise label(btex #1 etex,I); label(btex #2 etex,1.2[M,B]); label(btex #3 etex,1.2[N,C]); label(btex #4 etex,1.1[B,M]); label(btex #5 etex,1.1[C,N]); fill (fullcircle scaled 0.75mm) shifted (cotes5 intersectionpoint cotes4); fill (fullcircle scaled 0.75mm) shifted (cotes6 intersectionpoint cotes4); fill (fullcircle scaled 0.75mm) shifted (cotes1 intersectionpoint cotes2); fill (fullcircle scaled 0.75mm) shifted (cotes3 intersectionpoint cotes2); \end{mplibcode} % \mplibcodeinherit{disable} \else \begin{mpost}[mpsettings={u:=\useKV[ClesThales]{Echelle};}] pair A,B,C,M,N,O;% O=(2.5u,2.5u); path cc; cc=(fullcircle scaled 3u) shifted O; %On place les points A,B,C sur le cercle de mani\`ere \`a faciliter la rotation de la figure A=point(0.1*length cc) of cc; B=A rotatedabout(O,130); C=(A--2[A,B rotatedabout(A,45)]) intersectionpoint (B--2[B,A rotatedabout(B,-60)]); % On tourne pour \'eventuellement moins de lassitude :) A:=A rotatedabout(O,#6); B:=B rotatedabout(O,#6); C:=C rotatedabout(O,#6); % on dessine \`a main lev\'ee :) M=1.4[B,A]; N=1.4[C,A]; path cotes[]; cotes1=A{dir(angle(B-A)+5)}..1.15[A,B]{dir(angle(B-A)+5)}; cotes2=1.15[C,B]{dir(angle(C-B)+5)}..1.15[B,C]{dir(angle(C-B)+5)}; cotes3=1.15[A,C]{dir(angle(A-C)+5)}..A{dir(angle(A-C)+5)}; cotes4=1.5[N,M]{dir(angle(N-M)+5)}..1.5[M,N]{dir(angle(N-M)+5)}; cotes5=A{dir(angle(M-A)+5)}..1.15[A,M]{dir(angle(M-A)+5)}; cotes6=A{dir(angle(N-A)+5)}..1.15[A,N]{dir(angle(N-A)+5)}; for k=1 upto 6: draw cotes[k]; endfor; pair I; % On d\'efinit le centre du cercle inscrit \`a AMC (I-C) rotated ((angle(A-C)-angle(M-C))/2) shifted C=whatever[A,C]; (I-M) rotated ((angle(C-M)-angle(A-M))/2) shifted M=whatever[M,C]; %on labelise label(btex #1 etex,I); label(btex #2 etex,1.2[M,B]); label(btex #3 etex,1.2[N,C]); label(btex #4 etex,1.1[B,M]); label(btex #5 etex,1.1[C,N]); fill (fullcircle scaled 0.75mm) shifted (cotes5 intersectionpoint cotes4); fill (fullcircle scaled 0.75mm) shifted (cotes6 intersectionpoint cotes4); fill (fullcircle scaled 0.75mm) shifted (cotes1 intersectionpoint cotes2); fill (fullcircle scaled 0.75mm) shifted (cotes3 intersectionpoint cotes2); \end{mpost} \fi } \newcommand\RedactionThales{}% \newcommand\EcritureCalculs{}% \newcommand\EcritureQuotients{}% %%% \newcommand\TTThales[6][]{% \useKVdefault[ClesThales]% \setKV[ClesThales]{#1}% \ifboolKV[ClesThales]{Perso}{\RedactionThales}{% \ifboolKV[ClesThales]{Droites}{% Les droites \ifboolKV[ClesThales]{Remediation}{\pointilles[2cm]}{$(#3#5)$} et \ifboolKV[ClesThales]{Remediation}{\pointilles[2cm]}{$(#4#6)$} sont s\'ecantes en \ifboolKV[ClesThales]{Remediation}{\pointilles[2cm]}{$#2$}.% }{% Dans le triangle \ifboolKV[ClesThales]{Remediation}{\pointilles[2cm]}{$#2#3#4$}, \ifboolKV[ClesThales]{Remediation}{\pointilles[1cm]}{$#5$} est un point \ifboolKV[ClesThales]{Segment}{du segment}{de la droite} \ifboolKV[ClesThales]{Remediation}{\pointilles[2cm]}{\ifboolKV[ClesThales]{Segment}{$[#2#3]$}{$(#2#3)$}}, \ifboolKV[ClesThales]{Remediation}{\pointilles[1cm]}{$#6$} est un point \ifboolKV[ClesThales]{Segment}{du segment}{de la droite} \ifboolKV[ClesThales]{Remediation}{\pointilles[2cm]}{\ifboolKV[ClesThales]{Segment}{$[#2#4]$}{$(#2#4)$}}.% } \\Comme les droites \ifboolKV[ClesThales]{Remediation}{\pointilles[2cm]}{$(#5#6)$} et \ifboolKV[ClesThales]{Remediation}{\pointilles[2cm]}{$(#3#4)$} sont parall\`eles, alors \ifboolKV[ClesThales]{Propor}{le tableau% \[\begin{array}{c|c|c} \ifboolKV[ClesThales]{Remediation}{\pointilles[1cm]}{#2#5}&\ifboolKV[ClesThales]{Remediation}{\pointilles[1cm]}{#2#6}&\ifboolKV[ClesThales]{Remediation}{\pointilles[1cm]}{#5#6}\\ \hline \ifboolKV[ClesThales]{Remediation}{\pointilles[1cm]}{#2#3}&\ifboolKV[ClesThales]{Remediation}{\pointilles[1cm]}{#2#4}&\ifboolKV[ClesThales]{Remediation}{\pointilles[1cm]}{#3#4}\\ \end{array} \] est un tableau de proportionnalit\'e\ifboolKV[ClesThales]{Segment}{.}{ d'apr\`es le th\'eor\`eme de Thal\`es.}% }{% \ifboolKV[ClesThales]{Segment}{on a :}{le th\'eor\`eme de Thal\`es permet d'\'ecrire :}% \[\frac{\ifboolKV[ClesThales]{Remediation}{\pointilles[1cm]}{\ifboolKV[ClesThales]{CouleursNum}{\mathcolor{\useKV[ClesThales]{CouleurNum}}{#2#5}}{#2#5}}}{\ifboolKV[ClesThales]{Remediation}{\pointilles[1cm]}{\ifboolKV[ClesThales]{CouleursDen}{\mathcolor{\useKV[ClesThales]{CouleurDen}}{#2#3}}{#2#3}}}=\frac{\ifboolKV[ClesThales]{Remediation}{\pointilles[1cm]}{\ifboolKV[ClesThales]{CouleursNum}{\mathcolor{\useKV[ClesThales]{CouleurNum}}{#2#6}}{#2#6}}}{\ifboolKV[ClesThales]{Remediation}{\pointilles[1cm]}{\ifboolKV[ClesThales]{CouleursDen}{\mathcolor{\useKV[ClesThales]{CouleurDen}}{#2#4}}{#2#4}}}=\frac{\ifboolKV[ClesThales]{Remediation}{\pointilles[1cm]}{\ifboolKV[ClesThales]{CouleursNum}{\mathcolor{\useKV[ClesThales]{CouleurNum}}{#5#6}}{#5#6}}}{\ifboolKV[ClesThales]{Remediation}{\pointilles[1cm]}{\ifboolKV[ClesThales]{CouleursDen}{\mathcolor{\useKV[ClesThales]{CouleurDen}}{#3#4}}{#3#4}}}.\]% }% }% }% \newcommand\TThalesCalculsD[8][]{% \setKV[ClesThales]{#1}% \newcount\zzz\newcount\yyy\newcount\xxx%Pour se rappeller des calculs \`a faire et combien en faire% \def\Nomx{}% \def\Nomy{}% \def\Nomz{}% \zzz=0\yyy=0\xxx=0% \TTThales[#1]{\StrMid{#2}{1}{1}}{\StrMid{#2}{2}{2}}{\StrMid{#2}{3}{3}}{\StrMid{#2}{4}{4}}{\StrMid{#2}{5}{5}}\par \IfDecimal{#3}{% \IfDecimal{#6}{}{% \IfDecimal{#4}{% \IfDecimal{#7}{% \xxx=5263%#6&=\frac{#3\times#7}{#4}\\ \edef\Nomx{#6}\opcopy{#3}{valx}\opcopy{#7}{Valx}\opcopy{#4}{denox}% \xdef\ResultatThalesx{\fpeval{round(#3*#7/#4,\useKV[ClesThales]{Precision})}}% }{% \IfDecimal{#8}{\IfDecimal{#5}{\xxx=5274%\[#6=\frac{#3\times#8}{#5}\] \edef\Nomx{#6}\opcopy{#3}{valx}\opcopy{#8}{Valx}\opcopy{#5}{denox}% \xdef\ResultatThalesx{\fpeval{round(#3*#8/#5,\useKV[ClesThales]{Precision})}}% }{}}{} } }{\IfDecimal{#8}{\IfDecimal{#5}{\xxx=5274%\[#6=\frac{#3\times#8}{#5}\] \edef\Nomx{#6}\opcopy{#3}{valx}\opcopy{#8}{Valx}\opcopy{#5}{denox}% \xdef\ResultatThalesx{\fpeval{round(#3*#8/#5,\useKV[ClesThales]{Precision})}}% }{}}{} } } }{% \IfDecimal{#6}{% \IfDecimal{#4}{% \IfDecimal{#7}{% \xxx=2536%\[#3=\frac{#6\times#4}{#7}\]% \edef\Nomx{#3}\opcopy{#6}{valx}\opcopy{#4}{Valx}\opcopy{#7}{denox}% \xdef\ResultatThalesx{\fpeval{round(#6*#4/#7,\useKV[ClesThales]{Precision})}}% }{% \IfDecimal{#5}{\IfDecimal{#8}{\xxx=2547 \edef\Nomx{#3}\opcopy{#6}{valx}\opcopy{#5}{Valx}\opcopy{#8}{denox}%\[#3=\frac{#6\times#5}{#8}\] \xdef\ResultatThalesx{\fpeval{round(#6*#5/#8,\useKV[ClesThales]{Precision})}}% }{}}{} } }{\IfDecimal{#5}{\IfDecimal{#8}{\xxx=2547 \edef\Nomx{#3}\opcopy{#6}{valx}\opcopy{#5}{Valx}\opcopy{#8}{denox}%\[#3=\frac{#6\times#5}{#8}\] \xdef\ResultatThalesx{\fpeval{round(#6*#5/#8,\useKV[ClesThales]{Precision})}}% }{}}{} } }{} }% % \IfDecimal{#4}{% \IfDecimal{#7}{}{% \IfDecimal{#5}{% \IfDecimal{#8}{% \yyy=6374%\[#7=\frac{#4\times#8}{#5}\]% \edef\Nomy{#7}\opcopy{#4}{valy}\opcopy{#8}{Valy}\opcopy{#5}{denoy}% \xdef\ResultatThalesy{\fpeval{round(#4*#8/#5,\useKV[ClesThales]{Precision})}}% }{% \IfDecimal{#6}{\IfDecimal{#3}{\yyy=6352%\[#7=\frac{#4\times#6}{#3}\] \edef\Nomy{#7}\opcopy{#4}{valy}\opcopy{#6}{Valy}\opcopy{#3}{denoy}% \xdef\ResultatThalesy{\fpeval{round(#4*#6/#3,\useKV[ClesThales]{Precision})}}% }{}}{} } }{\IfDecimal{#6}{\IfDecimal{#3}{\yyy=6352%\[#7=\frac{#4\times#6}{#3}\] \edef\Nomy{#7}\opcopy{#4}{valy}\opcopy{#6}{Valy}\opcopy{#3}{denoy}% \xdef\ResultatThalesy{\fpeval{round(#4*#6/#3,\useKV[ClesThales]{Precision})}}% }{}}{} } } }{% \IfDecimal{#7}{% \IfDecimal{#5}{% \IfDecimal{#8}{% \yyy=3647%\[#4=\frac{#7\times#5}{#8}\]% \edef\Nomy{#4}\opcopy{#7}{valy}\opcopy{#5}{Valy}\opcopy{#8}{denoy}% \xdef\ResultatThalesy{\fpeval{round(#7*#5/#8,\useKV[ClesThales]{Precision})}}% }{% \IfDecimal{#3}{\IfDecimal{#6}{\yyy=3625%\[#4=\frac{#7\times#3}{#6}\] \edef\Nomy{#4}\opcopy{#7}{valy}\opcopy{#3}{Valy}\opcopy{#6}{denoy}% \xdef\ResultatThalesy{\fpeval{round(#7*#3/#6,\useKV[ClesThales]{Precision})}}% }{}}{} } }{\IfDecimal{#3}{\IfDecimal{#6}{\yyy=3625%\[#4=\frac{#7\times#3}{#6}\] \edef\Nomy{#4}\opcopy{#7}{valy}\opcopy{#3}{Valy}\opcopy{#6}{denoy}% \xdef\ResultatThalesy{\fpeval{round(#7*#3/#6,\useKV[ClesThales]{Precision})}}% }{}}{} }}{}}% % \IfDecimal{#5}{% \IfDecimal{#8}{}{% \IfDecimal{#4}{ \IfDecimal{#7}{ \zzz=7463%\[#8=\frac{#5\times#7}{#4}\]% \edef\Nomz{#8}\opcopy{#5}{valz}\opcopy{#7}{Valz}\opcopy{#4}{denoz}% \xdef\ResultatThalesz{\fpeval{round(#5*#7/#4,\useKV[ClesThales]{Precision})}}% }{% \IfDecimal{#3}{\IfDecimal{#6}{\zzz=7452%\[#8=\frac{#5\times#6}{#3}\] \edef\Nomz{#8}\opcopy{#5}{valz}\opcopy{#6}{Valz}\opcopy{#3}{denoz}% \xdef\ResultatThalesz{\fpeval{round(#5*#6/#3,\useKV[ClesThales]{Precision})}}% }{}}{} } }{\IfDecimal{#3}{\IfDecimal{#6}{\zzz=7452%\[#8=\frac{#5\times#6}{#3}\] \edef\Nomz{#8}\opcopy{#5}{valz}\opcopy{#6}{Valz}\opcopy{#3}{denoz}% \xdef\ResultatThalesz{\fpeval{round(#5*#6/#3,\useKV[ClesThales]{Precision})}}% }{}}{} } } }{% \IfDecimal{#8}{% \IfDecimal{#4}{% \IfDecimal{#7}{% \zzz=4736% \[#5=\frac{#8\times#4}{#7}\]% \edef\Nomz{#5}\opcopy{#8}{valz}\opcopy{#4}{Valz}\opcopy{#7}{denoz}% \xdef\ResultatThalesz{\fpeval{round(#8*#4/#7,\useKV[ClesThales]{Precision})}}% }{% \IfDecimal{#3}{\IfDecimal{#6}{\zzz=4725%\[#5=\frac{#8\times#3}{#6}\] \edef\Nomz{#5}\opcopy{#8}{valz}\opcopy{#3}{Valz}\opcopy{#6}{denoz}% \xdef\ResultatThalesz{\fpeval{round(#8*#3/#6,\useKV[ClesThales]{Precision})}}% }{}}{} } }{\IfDecimal{#3}{\IfDecimal{#6}{\zzz=4725%\[#5=\frac{#8\times#3}{#6}\] \edef\Nomz{#5}\opcopy{#8}{valz}\opcopy{#3}{Valz}\opcopy{#6}{denoz}% \xdef\ResultatThalesz{\fpeval{round(#8*#3/#6,\useKV[ClesThales]{Precision})}}% }{}}{} }}{} }% %% \StrMid{\the\zzz}{1}{1}[\cmza]% \StrMid{\the\yyy}{1}{1}[\cmya]% \StrMid{\the\xxx}{1}{1}[\cmxa]% \ifboolKV[ClesThales]{Calcul}{% %%%%%%%%%%%%%%%%%%%%%%%%%%% \ifboolKV[ClesThales]{IntroCalculs}{On remplace par les longueurs connues :}{}% \ifboolKV[ClesThales]{CalculsPerso}{% \EcritureQuotients% }{% \ifboolKV[ClesThales]{Propor}{% \[\begin{array}{c|c|c} \IfDecimal{#3}{\num{#3}}{#3}&\IfDecimal{#4}{\num{#4}}{#4}&\IfDecimal{#5}{\num{#5}}{#5}\\ \hline \IfDecimal{#6}{\num{#6}}{#6}&\IfDecimal{#7}{\num{#7}}{#7}&\IfDecimal{#8}{\num{#8}}{#8} \end{array} \] }{% \[\frac{\IfDecimal{#3}{\num{#3}}{#3}}{\IfDecimal{#6}{\num{#6}}{#6}}=\frac{\IfDecimal{#4}{\num{#4}}{#4}}{\IfDecimal{#7}{\num{#7}}{#7}}=\frac{\IfDecimal{#5}{\num{#5}}{#5}}{\IfDecimal{#8}{\num{#8}}{#8}}\] }% }% % On choisit \'eventuellement le calcul \`a faire s'il y en a plusieurs. \xdef\CompteurCalcul{\useKV[ClesThales]{ChoixCalcul}}% \xintifboolexpr{\CompteurCalcul>0}{\xintifboolexpr{\CompteurCalcul==1}{\xdef\cmya{0}\xdef\cmza{0}}{\xintifboolexpr{\CompteurCalcul==2}{\xdef\cmxa{0}\xdef\cmza{0}}{\xdef\cmxa{0}\xdef\cmya{0}}}}{}% %% on fait les calculs \ifboolKV[ClesThales]{CalculsPerso}{% \EcritureCalculs% }{% \begin{align*} % Premier compteur \xxx \ifnum\cmxa>0 \Nomx\uppercase{&}=\frac{\opexport{valx}{\valx}\num{\valx}\times\opexport{Valx}{\Valx}\num{\Valx}}{\opexport{denox}{\denox}\num{\denox}}\relax%\global\numx=\numexpr\opprint{valx}*\opprint{Valx}\relax \fi % % Deuxi\`eme compteur \yyy \ifnum\cmya>0 \ifnum\cmxa=0 \else \uppercase{&} \fi% \Nomy\uppercase{&}=\frac{\opexport{valy}{\valy}\num{\valy}\times\opexport{Valy}{\Valy}\num{\Valy}}{\opexport{denoy}{\denoy}\num{\denoy}}\relax%\global\numy=\numexpr\opprint{valy}*\opprint{Valy}\relax \fi % Troisi\`eme compteur \zzz \ifnum\cmza>0 \ifnum\cmxa=0 \ifnum\cmya=0 % \else \uppercase{&} \fi \Nomz\uppercase{&}=\frac{\opexport{valz}{\valz}\num{\valz}\times\opexport{Valz}{\Valz}\num{\Valz}}{\opexport{denoz}{\denoz}\num{\denoz}}\relax%\global\numz=\numexpr\opprint{valz}*\opprint{Valz}\relax \else \uppercase{&}\Nomz\uppercase{&}=\frac{\opexport{valz}{\valz}\num{\valz}\times\opexport{Valz}{\Valz}\num{\Valz}}{\opexport{denoz}{\denoz}\num{\denoz}}\relax%\global\numz=\numexpr\opprint{valz}*\opprint{Valz}\relax \fi \fi \\ % % 2eme ligne du tableau : calcul des num\'erateurs % %Premier compteur \xxx \ifnum\cmxa>0 \Nomx\uppercase{&}=\frac{\opmul*{valx}{Valx}{numx}\opexport{numx}{\numx}\num{\numx}}{\opexport{denox}{\denox}\num{\denox}} \fi % % Deuxi\`eme compteur \yyy \ifnum\cmya>0 \ifnum\cmxa=0 % \else \uppercase{&} \fi \Nomy\uppercase{&}=\frac{\opmul*{valy}{Valy}{numy}\opexport{numy}{\numy}\num{\numy}}{\opexport{denoy}{\denoy}\num{\denoy}}% \fi % %Troisi\`eme compteur \zzz \ifnum\cmza>0 \ifnum\cmxa=0 \ifnum\cmya=0 % \else \uppercase{&} \fi \Nomz\uppercase{&}=\frac{\opmul*{valz}{Valz}{numz}\opexport{numz}{\numz}\num{\numz}}{\opexport{denoz}{\denoz}\num{\denoz}} \else \uppercase{&}\Nomz\uppercase{&}=\frac{\opmul*{valz}{Valz}{numz}\opexport{numz}{\numz}\num{\numz}}{\opexport{denoz}{\denoz}\num{\denoz}} \fi \fi \\ % % 3eme ligne : Calculs \ifnum\cmxa>0 \Nomx\uppercase{&}\opdiv*{numx}{denox}{resultatx}{restex}\opcmp{restex}{0}\ifopeq=\SI{\ResultatThalesx}{\PfCThalesUnit}\else\approx\SI{\fpeval{round(\ResultatThalesx,\useKV[ClesThales]{Precision})}}{\PfCThalesUnit}\fi% \fi % % Deuxi\`eme compteur \yyy \ifnum\cmya>0 \ifnum\cmxa=0 % \else \uppercase{&} \fi \Nomy\uppercase{&}\opdiv*{numy}{denoy}{resultaty}{restey}\opcmp{restey}{0}\ifopeq=\SI{\ResultatThalesy}{\PfCThalesUnit}\else\approx\SI{\fpeval{round(\ResultatThalesy,\useKV[ClesThales]{Precision})}}{\PfCThalesUnit}\fi% \fi % %Troisi\`eme compteur \zzz \ifnum\cmza>0 \ifnum\cmxa=0 \ifnum\cmya=0 % \else \uppercase{&} \fi \Nomz\uppercase{&}\opdiv*{numz}{denoz}{resultatz}{restez}\opcmp{restez}{0}\ifopeq=\SI{\ResultatThalesz}{\PfCThalesUnit}\else\approx\SI{\fpeval{round(\ResultatThalesz,\useKV[ClesThales]{Precision})}}{\PfCThalesUnit}\fi% \else \uppercase{&}\Nomz\uppercase{&}\opdiv*{numz}{denoz}{resultatz}{restez}\opcmp{restez}{0}\ifopeq=\SI{\ResultatThalesz}{\PfCThalesUnit}\else\approx\SI{\fpeval{round(\ResultatThalesz,\useKV[ClesThales]{Precision})}}{\PfCThalesUnit}\fi% \fi \fi \end{align*} } }{} } \newcommand\TThalesCalculsE[8][]{% \setKV[ClesThales]{#1}% \newcount\zzz\newcount\yyy\newcount\xxx%Pour se rappeller des calculs \`a faire et combien en faire% \newcount\valx\newcount\Valx% \newcount\valy\newcount\Valy% \newcount\valz\newcount\Valz% \newcount\numx\newcount\numy\newcount\numz% \newcount\denox\newcount\denoy\newcount\denoz% \def\Nomx{}% \def\Nomy{}% \def\Nomz{}% \zzz=0\yyy=0\xxx=0% \TTThales[#1]{\StrMid{#2}{1}{1}}{\StrMid{#2}{2}{2}}{\StrMid{#2}{3}{3}}{\StrMid{#2}{4}{4}}{\StrMid{#2}{5}{5}}\par% \IfDecimal{#3}{% \IfDecimal{#6}{}{% \IfDecimal{#4}{% \IfDecimal{#7}{% \xxx=5263%#6&=\frac{#3\times#7}{#4}\\ \edef\Nomx{#6}\valx=#3\Valx=#7\denox=#4% }{% \IfDecimal{#8}{\IfDecimal{#5}{\xxx=5274%\[#6=\frac{#3\times#8}{#5}\] \edef\Nomx{#6}\valx=#3\Valx=#8\denox=#5% }{}}{} } }{\IfDecimal{#8}{\IfDecimal{#5}{\xxx=5274%\[#6=\frac{#3\times#8}{#5}\] \edef\Nomx{#6}\valx=#3\Valx=#8\denox=#5% }{}}{} } } }{% \IfDecimal{#6}{% \IfDecimal{#4}{% \IfDecimal{#7}{% \xxx=2536%\[#3=\frac{#6\times#4}{#7}\]% \edef\Nomx{#3}\valx=#6\Valx=#4\denox=#7% }{% \IfDecimal{#5}{\IfDecimal{#8}{\xxx=2547 \edef\Nomx{#3}\valx=#6\Valx=#5\denox=#8%\[#3=\frac{#6\times#5}{#8}\] }{}}{} } }{\IfDecimal{#5}{\IfDecimal{#8}{\xxx=2547 \edef\Nomx{#3}\valx=#6\Valx=#5\denox=#8%\[#3=\frac{#6\times#5}{#8}\] }{}}{} } }{} }% % \IfDecimal{#4}{% \IfDecimal{#7}{}{% \IfDecimal{#5}{% \IfDecimal{#8}{% \yyy=6374%\[#7=\frac{#4\times#8}{#5}\]% \edef\Nomy{#7}\valy=#4\Valy=#8\denoy=#5% }{% \IfDecimal{#6}{\IfDecimal{#3}{\yyy=6352%\[#7=\frac{#4\times#6}{#3}\] \edef\Nomy{#7}\valy=#4\Valy=#6\denoy=#3% }{}}{} } }{\IfDecimal{#6}{\IfDecimal{#3}{\yyy=6352%\[#7=\frac{#4\times#6}{#3}\] \edef\Nomy{#7}\valy=#4\Valy=#6\denoy=#3% }{}}{} } } }{% \IfDecimal{#7}{% \IfDecimal{#5}{% \IfDecimal{#8}{% \yyy=3647%\[#4=\frac{#7\times#5}{#8}\]% \edef\Nomy{#4}\valy=#7\Valy=#5\denoy=#8% }{% \IfDecimal{#3}{\IfDecimal{#6}{\yyy=3625%\[#4=\frac{#7\times#3}{#6}\] \edef\Nomy{#4}\valy=#7\Valy=#3\denoy=#6% }{}}{} } }{\IfDecimal{#3}{\IfDecimal{#6}{\yyy=3625%\[#4=\frac{#7\times#3}{#6}\] \edef\Nomy{#4}\valy=#7\Valy=#3\denoy=#6% }{}}{} }}{}}% % \IfDecimal{#5}{% \IfDecimal{#8}{}{% \IfDecimal{#4}{ \IfDecimal{#7}{ \zzz=7463%\[#8=\frac{#5\times#7}{#4}\]% \edef\Nomz{#8}\valz=#5\Valz=#7\denoz=#4% }{% \IfDecimal{#3}{\IfDecimal{#6}{\zzz=7452%\[#8=\frac{#5\times#6}{#3}\] \edef\Nomz{#8}\valz=#5\Valz=#6\denoz=#3% }{}}{} } }{\IfDecimal{#3}{\IfDecimal{#6}{\zzz=7452%\[#8=\frac{#5\times#6}{#3}\] \edef\Nomz{#8}\valz=#5\Valz=#6\denoz=#3% }{}}{} } } }{% \IfDecimal{#8}{% \IfDecimal{#4}{% \IfDecimal{#7}{% \zzz=4736% \[#5=\frac{#8\times#4}{#7}\]% \edef\Nomz{#5}\valz=#8\Valz=#4\denoz=#7% }{% \IfDecimal{#3}{\IfDecimal{#6}{\zzz=4725%\[#5=\frac{#8\times#3}{#6}\] \edef\Nomz{#5}\valz=#8\Valz=#3\denoz=#6% }{}}{} } }{\IfDecimal{#3}{\IfDecimal{#6}{\zzz=4725%\[#5=\frac{#8\times#3}{#6}\] \edef\Nomz{#5}\valz=#8\Valz=#3\denoz=#6% }{}}{} }}{} }% %% \StrMid{\the\zzz}{1}{1}[\cmza]% \StrMid{\the\yyy}{1}{1}[\cmya]% \StrMid{\the\xxx}{1}{1}[\cmxa]% \ifboolKV[ClesThales]{Calcul}{% %%%%%%%%%%%%%%%%%%%%%%%%%%% On remplace par les longueurs connues : \ifboolKV[ClesThales]{Propor}{% \[\begin{array}{c|c|c} \IfDecimal{#3}{\num{#3}}{#3}&\IfDecimal{#4}{\num{#4}}{#4}&\IfDecimal{#5}{\num{#5}}{#5}\\ \hline \IfDecimal{#6}{\num{#6}}{#6}&\IfDecimal{#7}{\num{#7}}{#7}&\IfDecimal{#8}{\num{#8}}{#8}\\ \end{array} \] }{% \[\frac{\IfDecimal{#3}{\num{#3}}{#3}}{\IfDecimal{#6}{\num{#6}}{#6}}=\frac{\IfDecimal{#4}{\num{#4}}{#4}}{\IfDecimal{#7}{\num{#7}}{#7}}=\frac{\IfDecimal{#5}{\num{#5}}{#5}}{\IfDecimal{#8}{\num{#8}}{#8}}.\] }% % On choisit \'eventuellement le calcul \`a faire s'il y en a plusieurs. \xdef\CompteurCalcul{\useKV[ClesThales]{ChoixCalcul}}% \xintifboolexpr{\CompteurCalcul>0}{\xintifboolexpr{\CompteurCalcul==1}{\xdef\cmya{0}\xdef\cmza{0}}{\xintifboolexpr{\CompteurCalcul==2}{\xdef\cmxa{0}\xdef\cmza{0}}{\xdef\cmxa{0}\xdef\cmya{0}}}}% %%on fait les calculs \begin{align*} %Premier compteur \xxx \ifnum\cmxa>0 \Nomx\uppercase{&}=\frac{\the\valx\times\the\Valx}{\the\denox}\global\numx=\numexpr\the\valx*\the\Valx\relax \fi % % Deuxi\`eme compteur \yyy \ifnum\cmya>0 \ifnum\cmxa=0 \else \uppercase{&} \fi% \Nomy\uppercase{&}=\frac{\the\valy\times\the\Valy}{\the\denoy}\global\numy=\numexpr\the\valy*\the\Valy\relax % \else % \uppercase{&}\Nomy\uppercase{&}=\frac{\the\valy\times\the\Valy}{\the\denoy}\global\numy=\numexpr\the\valy*\the\Valy\relax % \fi \fi % Troisi\`eme compteur \zzz \ifnum\cmza>0 \ifnum\cmxa=0 \ifnum\cmya=0 %\Nomz\uppercase{&}=\frac{\the\valz\times\the\Valz}{\the\denoz}\global\numz=\numexpr\the\valz*\the\Valz\relax \else \uppercase{&}%\Nomz\uppercase{&}=\frac{\the\valz\times\the\Valz}{\the\denoz}\global\numz=\numexpr\the\valz*\the\Valz\relax \fi \Nomz\uppercase{&}=\frac{\the\valz\times\the\Valz}{\the\denoz}\global\numz=\numexpr\the\valz*\the\Valz\relax \else \uppercase{&}\Nomz\uppercase{&}=\frac{\the\valz\times\the\Valz}{\the\denoz}\global\numz=\numexpr\the\valz*\the\Valz\relax \fi \fi \\ % 2eme ligne du tableau : calcul des num\'erateurs %Premier compteur \xxx \ifnum\cmxa>0 \Nomx\uppercase{&}=\frac{\num{\the\numx}}{\num{\the\denox}} \fi % % Deuxi\`eme compteur \yyy \ifnum\cmya>0 \ifnum\cmxa=0 %\Nomy\uppercase{&}=\frac{\num{\the\numy}}{\num{\the\denoy}} \else \uppercase{&}%\Nomy\uppercase{&}=\frac{\num{\the\numy}}{\num{\the\denoy}} \fi \Nomy\uppercase{&}=\frac{\num{\the\numy}}{\num{\the\denoy}}% \fi %Troisi\`eme compteur \zzz \ifnum\cmza>0 \ifnum\cmxa=0 \ifnum\cmya=0 %\Nomz\uppercase{&}=\frac{\num{\the\numz}}{\num{\the\denoz}} \else \uppercase{&}%\Nomz\uppercase{&}=\frac{\num{\the\numz}}{\num{\the\denoz}} \fi \Nomz\uppercase{&}=\frac{\num{\the\numz}}{\num{\the\denoz}} \else \uppercase{&}\Nomz\uppercase{&}=\frac{\num{\the\numz}}{\num{\the\denoz}} \fi \fi \\ % 3eme ligne : faire les simplifications ou pas ? %Premier compteur \xxx \ifnum\cmxa>0 \PGCD{\the\numx}{\the\denox} \ifnum\pgcd>1 \Nomx\uppercase{&}=\SSimpli{\the\numx}{\the\denox} \else \uppercase{&} \fi \fi % % Deuxi\`eme compteur \yyy \ifnum\cmya>0 \PGCD{\the\numy}{\the\denoy} \ifnum\cmxa=0 \ifnum\pgcd>1 \Nomy\uppercase{&}=\SSimpli{\the\numy}{\the\denoy} \else \uppercase{&} \fi \else \ifnum\pgcd>1 \uppercase{&}\Nomy\uppercase{&}=\SSimpli{\the\numy}{\the\denoy} \else \uppercase{&&} \fi \fi \fi %Troisi\`eme compteur \zzz \ifnum\cmza>0 \PGCD{\the\numz}{\the\denoz} \ifnum\cmxa=0 \ifnum\cmya=0 \ifnum\pgcd>1 \Nomz\uppercase{&}=\SSimpli{\the\numz}{\the\denoz} \else \uppercase{&} \fi \else \ifnum\pgcd>1 \uppercase{&}\Nomz\uppercase{&}=\SSimpli{\the\numz}{\the\denoz} \else \uppercase{&&} \fi \fi \else \ifnum\pgcd>1 \uppercase{&}\Nomz\uppercase{&}=\SSimpli{\the\numz}{\the\denoz} \else \uppercase{&&} \fi \fi \fi \\ % 4eme ligne : Terminer les simplifications ? %Premier compteur \xxx \ifnum\cmxa>0 \PGCD{\the\numx}{\the\denox} \ifnum\pgcd>1 \ifnum\pgcd<\the\denox \Nomx\uppercase{&}=\SSimplifie{\the\numx}{\the\denox} \else \uppercase{&} \fi \else \uppercase{&} \fi \fi % % Deuxi\`eme compteur \yyy \ifnum\cmya>0 \PGCD{\the\numy}{\the\denoy} \ifnum\cmxa=0 \ifnum\pgcd>1 \ifnum\pgcd<\the\denoy \Nomy\uppercase{&}=\SSimplifie{\the\numy}{\the\denoy} \else \uppercase{&} \fi \else \uppercase{&} \fi \else \ifnum\pgcd>1 \ifnum\pgcd<\the\denoy \uppercase{&}\Nomy\uppercase{&}=\SSimplifie{\the\numy}{\the\denoy} \else \uppercase{&&} \fi \else \uppercase{&&} \fi \fi \fi %Troisi\`eme compteur \zzz \ifnum\cmza>0 \PGCD{\the\numz}{\the\denoz} \ifnum\cmxa=0 \ifnum\cmya=0 \ifnum\pgcd>1 \ifnum\pgcd<\the\denoz \Nomz\uppercase{&}=\SSimplifie{\the\numz}{\the\denoz} \else \uppercase{&} \fi \else \uppercase{&} \fi \else \ifnum\pgcd>1 \ifnum\pgcd<\the\denoz \uppercase{&}\Nomz\uppercase{&}=\SSimplifie{\the\numz}{\the\denoz} \else \uppercase{&&} \fi \else \uppercase{&&} \fi \fi \else \ifnum\pgcd>1 \ifnum\pgcd<\the\denoz \uppercase{&}\Nomz\uppercase{&}=\SSimplifie{\the\numz}{\the\denoz} \else \uppercase{&&} \fi \else \uppercase{&&} \fi \fi \fi%\\ \end{align*} }{}% } \newcommand\TThales[8][]{% \setKV[ClesThales]{#1}% \StrMid{#2}{1}{1}[\NomA]\StrMid{#2}{2}{2}[\NomB]\StrMid{#2}{3}{3}[\NomC]\StrMid{#2}{4}{4}[\NomM]\StrMid{#2}{5}{5}[\NomN]% \ifboolKV[ClesThales]{FigureSeule}{% \MPFigThales{\NomA}{\NomB}{\NomC}{\NomM}{\NomN}{\useKV[ClesThales]{Angle}}% }{\ifboolKV[ClesThales]{FigurecroiseeSeule}{% \MPFigThalesCroisee{\NomA}{\NomB}{\NomC}{\NomM}{\NomN}{\useKV[ClesThales]{Angle}}% }{% \ifboolKV[ClesThales]{Figure}{% \StrMid{#2}{1}{1}[\NomA]\StrMid{#2}{2}{2}[\NomB]\StrMid{#2}{3}{3}[\NomC]\StrMid{#2}{4}{4}[\NomM]\StrMid{#2}{5}{5}[\NomN]% \begin{multicols}{2}% {\em La figure est donn\'ee \`a titre indicatif.}% \[\MPFigThales{\NomA}{\NomB}{\NomC}{\NomM}{\NomN}{\useKV[ClesThales]{Angle}}\]% \par\columnbreak\par% \ifboolKV[ClesThales]{Entier}{\TThalesCalculsE[#1]{#2}{#3}{#4}{#5}{#6}{#7}{#8}}{\TThalesCalculsD[#1]{#2}{#3}{#4}{#5}{#6}{#7}{#8}}% \end{multicols}% }{\ifboolKV[ClesThales]{Figurecroisee}{% \StrMid{#2}{1}{1}[\NomA]\StrMid{#2}{2}{2}[\NomB]\StrMid{#2}{3}{3}[\NomC]\StrMid{#2}{4}{4}[\NomM]\StrMid{#2}{5}{5}[\NomN]% \begin{multicols}{2}% {\em La figure est donn\'ee \`a titre indicatif.}% \[\MPFigThalesCroisee{\NomA}{\NomB}{\NomC}{\NomM}{\NomN}{\useKV[ClesThales]{Angle}}\]% \par\columnbreak\par% \ifboolKV[ClesThales]{Entier}{\TThalesCalculsE[#1]{#2}{#3}{#4}{#5}{#6}{#7}{#8}}{\TThalesCalculsD[#1]{#2}{#3}{#4}{#5}{#6}{#7}{#8}}% \end{multicols}% }{\ifboolKV[ClesThales]{Entier}{\TThalesCalculsE[#1]{#2}{#3}{#4}{#5}{#6}{#7}{#8}}{\TThalesCalculsD[#1]{#2}{#3}{#4}{#5}{#6}{#7}{#8}}}% }% }% }% }% %%%% \newcommand\ReciThales[6][]{% \ifboolKV[ClesThales]{Droites}{% Les droites $(#3#5)$ et $(#4#6)$ sont s\'ecantes en $#2$. }{% Dans le triangle $#2#3#4$, $#5$ est un point \ifboolKV[ClesThales]{Segment}{du segment $[#2#3]$}{de la droite $(#2#3)$}, $#6$ est un point \ifboolKV[ClesThales]{Segment}{du segment $[#2#4]$}{de la droite $(#2#4)$}. } % \ifboolKV[ClesThales]{Propor}{Le tableau $\begin{array}{c|c} #2#5#6\\ \hline #2#3#4\\ \end{array} $ est-il un tableau de proportionnalit\'e ? }{% } } \newcommand\ReciThalesCalculs[8][]{% \StrMid{#2}{1}{1}[\NomA]% \StrMid{#2}{2}{2}[\NomB]% \StrMid{#2}{3}{3}[\NomC]% \StrMid{#2}{4}{4}[\NomM]% \StrMid{#2}{5}{5}[\NomN]% \ifboolKV[ClesThales]{Produit}{% \begin{align*} \dfrac{\NomA\NomM}{\NomA\NomB}=\dfrac{\num{#3}}{\num{#4}}&&\dfrac{\NomA\NomN}{\NomA\NomC}=\dfrac{\num{#5}}{\num{#6}} \end{align*} Effectuons les produits en croix :\xdef\NumA{\fpeval{#3*#6}}\xdef\NumB{\fpeval{#4*#5}} \begin{align*} \num{#3}\times\num{#6}&=\num{\fpeval{#3*#6}}&&&\num{#4}\times\num{#5}&=\num{\fpeval{#4*#5}} \end{align*} \xintifboolexpr{\NumA == \NumB}{Comme les produits en croix sont \'egaux, alors $\dfrac{\NomA\NomM}{\NomA\NomB}=\dfrac{\NomA\NomN}{\NomA\NomC}$.\\[0.5em]% }{% Comme les produits en croix sont diff\'erents, alors $\dfrac{\NomA\NomM}{\NomA\NomB}\not=\dfrac{\NomA\NomN}{\NomA\NomC}$.\\% }% }{% \[\left. \begin{array}{l} \dfrac{\NomA\NomM}{\NomA\NomB}=\dfrac{\num{#3}}{\num{#4}}\ifx\bla#7\bla\ifboolKV[ClesThales]{Simplification}{\PGCD{#3}{#4}\xintifboolexpr{\pgcd==1}{%il faut regarder si on doit continuer avec le PPCM... \PGCD{#5}{#6}\xintifboolexpr{\pgcd>1}{\xdef\DenomSimpaa{\fpeval{#6/\pgcd}}\PPCM{#4}{\DenomSimpaa}\xintifboolexpr{\ppcm==#4}{}{=\dfrac{#3\times\num{\fpeval{\ppcm/#4}}}{#4\times\num{\fpeval{\ppcm/#4}}}=\dfrac{\num{\fpeval{#3*\ppcm/#4}}}{\num{\fpeval{\ppcm}}}}}{}% }{=\displaystyle\Simplification[All]{#3}{#4}\PGCD{#3}{#4}\xdef\NumSimp{\fpeval{#3/\pgcd}}\xdef\DenomSimp{\fpeval{#4/\pgcd}}\PGCD{#5}{#6}\xdef\NumSimpa{\fpeval{#5/\pgcd}}\xdef\DenomSimpa{\fpeval{#6/\pgcd}}\PPCM{\DenomSimp}{\DenomSimpa}\xintifboolexpr{\fpeval{\the\ppcm/\DenomSimp}==1}{}{=\dfrac{\num{\NumSimp}\times\num{\fpeval{\the\ppcm/\DenomSimp}}}{\num{\DenomSimp}\times\PPCM{\DenomSimp}{\DenomSimpa}\num{\fpeval{\the\ppcm/\DenomSimp}}}=\dfrac{\PPCM{\DenomSimp}{\DenomSimpa}\num{\fpeval{\NumSimp*\the\ppcm/\DenomSimp}}}{\PPCM{\DenomSimp}{\DenomSimpa}\num{\the\ppcm}}}}}{\PPCM{#4}{#6}\xintifboolexpr{\fpeval{\the\ppcm/#4}==1}{}{=\dfrac{\num{#3}\times\num{\fpeval{\the\ppcm/#4}}}{\num{#4}\times\PPCM{#4}{#6}\num{\fpeval{\the\ppcm/#4}}}=\dfrac{\PPCM{#4}{#6}\num{\fpeval{#3*\the\ppcm/#4}}}{\PPCM{#4}{#6}\num{\the\ppcm}}}}\xdef\NumA{\fpeval{#3*#6}}\else% \xintifboolexpr{#7==1}{}{=\dfrac{\num{#3}\times\num{#7}}{\num{#4}\times\num{#7}}=\dfrac{\num{\fpeval{#3*#7}}}{\num{\fpeval{#4*#7}}}}\xdef\NumC{\fpeval{#4*#7}}\xdef\NumD{\fpeval{#6*#8}}\PPCM{\NumC}{\NumD}\xintifboolexpr{\the\ppcm==\fpeval{#4*#7}}{}{=\dfrac{\num{\fpeval{#3*#7}}\times\num{\fpeval{\the\ppcm/(#4*#7)}}}{\num{\fpeval{#4*#7}}\times\xdef\NumC{\fpeval{#4*#7}}\xdef\NumD{\fpeval{#6*#8}}\PPCM{\NumC}{\NumD}\num{\fpeval{\the\ppcm/(#4*#7)}}}=\dfrac{\xdef\NumC{\fpeval{#4*#7}}\xdef\NumD{\fpeval{#6*#8}}\PPCM{\NumC}{\NumD}\num{\fpeval{#3*\the\ppcm/#4}}}{\xdef\NumC{\fpeval{#4*#7}}\xdef\NumD{\fpeval{#6*#8}}\PPCM{\NumC}{\NumD}\num{\fpeval{\the\ppcm}}}}\xdef\NumA{\fpeval{#3*#7*#6*#8}} \fi \\ \\ \dfrac{\NomA\NomN}{\NomA\NomC}=\dfrac{\num{#5}}{\num{#6}}% \ifx\bla#8\bla% \ifboolKV[ClesThales]{Simplification}{\PGCD{#5}{#6}\xintifboolexpr{\pgcd==1}{%il faut regarder si on doit continuer avec le PPCM... \PGCD{#3}{#4}\xintifboolexpr{\pgcd>1}{\xdef\DenomSimpaa{\fpeval{#4/\pgcd}}\PPCM{#6}{\DenomSimpaa}\xintifboolexpr{\ppcm==#6}{}{=\dfrac{#5\times\num{\fpeval{\ppcm/#6}}}{#6\times\num{\fpeval{\ppcm/#6}}}=\dfrac{\num{\fpeval{#5*\ppcm/#6}}}{\num{\fpeval{\ppcm}}}}}{}% }{=\displaystyle\Simplification[All]{#5}{#6}\PGCD{#5}{#6}\xdef\NumSimp{\fpeval{#5/\pgcd}}\xdef\DenomSimp{\fpeval{#6/\pgcd}}\PGCD{#3}{#4}\xdef\NumSimpa{\fpeval{#3/\pgcd}}\xdef\DenomSimpa{\fpeval{#4/\pgcd}}\PPCM{\DenomSimp}{\DenomSimpa}\xintifboolexpr{\fpeval{\the\ppcm/\DenomSimp}==1}{}{=\dfrac{\num{\NumSimp}\times\num{\fpeval{\the\ppcm/\DenomSimp}}}{\num{\DenomSimp}\times\PPCM{\DenomSimp}{\DenomSimpa}\num{\fpeval{\the\ppcm/\DenomSimp}}}=\dfrac{\PPCM{\DenomSimp}{\DenomSimpa}\num{\fpeval{\NumSimp*\the\ppcm/\DenomSimp}}}{\PPCM{\DenomSimp}{\DenomSimpa}\num{\the\ppcm}}}}}{\PPCM{#4}{#6}\xintifboolexpr{\fpeval{\the\ppcm/#6}==1}{}{=\dfrac{\num{#5}\times\num{\fpeval{\the\ppcm/#6}}}{\num{#6}\times\PPCM{#4}{#6}\num{\fpeval{\the\ppcm/#6}}}=\dfrac{\PPCM{#4}{#6}\num{\fpeval{#5*\the\ppcm/#6}}}{\PPCM{#4}{#6}\num{\the\ppcm}}}}\xdef\NumB{\fpeval{#5*#4}}% \else% \xintifboolexpr{#8==1}{}{=\dfrac{\num{#5}\times\num{#8}}{\num{#6}\times\num{#8}}=\dfrac{\num{\fpeval{#5*#8}}}{\num{\fpeval{#6*#8}}}}\xdef\NumC{\fpeval{#4*#7}}\xdef\NumD{\fpeval{#6*#8}}\PPCM{\NumC}{\NumD}\xintifboolexpr{\the\ppcm==\fpeval{#6*#8}}{}{=\dfrac{\num{\fpeval{#5*#8}}\times\num{\fpeval{\the\ppcm/(#6*#8)}}}{\num{\fpeval{#6*#8}}\times\xdef\NumC{\fpeval{#4*#7}}\xdef\NumD{\fpeval{#6*#8}}\PPCM{\NumC}{\NumD}\num{\fpeval{\the\ppcm/(#6*#8)}}}=\dfrac{\xdef\NumC{\fpeval{#4*#7}}\xdef\NumD{\fpeval{#6*#8}}\PPCM{\NumC}{\NumD}\num{\fpeval{#5*\the\ppcm/#6}}}{\xdef\NumC{\fpeval{#4*#7}}\xdef\NumD{\fpeval{#6*#8}}\PPCM{\NumC}{\NumD}\num{\fpeval{\the\ppcm}}} }\xdef\NumB{\fpeval{#5*#8*#4*#7}} \fi\\ \end{array} \right\}\ifnum\NumA=\NumB \dfrac{\NomA\NomM}{\NomA\NomB}=\dfrac{\NomA\NomN}{\NomA\NomC}\else\dfrac{\NomA\NomM}{\NomA\NomB}\not=\dfrac{\NomA\NomN}{\NomA\NomC}\fi \] }% \ifboolKV[ClesThales]{Propor}{% \xintifboolexpr{\NumA==\NumB}{Donc le tableau $\begin{array}{c|c} \NomA\NomM&\NomA\NomN\\ \hline \NomA\NomB&\NomA\NomC\\ \end{array} $ est bien un tableau de proportionnalit\'e.\\De plus, les points $\NomA$, $\NomM$, $\NomB$ sont align\'es dans le m\^eme ordre que les points $\NomA$, $\NomN$, $\NomC$. Donc les droites $(\NomM\NomN)$ et $(\NomB\NomC)$ sont parall\`eles d'apr\`es la r\'eciproque du th\'eor\`eme de Thal\`es.}{% Donc les droites $(\NomM\NomN)$ et $(\NomB\NomC)$ ne sont pas parall\`eles.}% }{% \xintifboolexpr{\NumA==\NumB}{% De plus, les points $\NomA$, $\NomM$, $\NomB$ sont align\'es dans le m\^eme ordre que les points $\NomA$, $\NomN$, $\NomC$. Donc les droites $(\NomM\NomN)$ et $(\NomB\NomC)$ sont parall\`eles d'apr\`es la r\'eciproque du th\'eor\`eme de Thal\`es.}{% Donc les droites $(\NomM\NomN)$ et $(\NomB\NomC)$ ne sont pas parall\`eles.}% }% }% \newcommand\ReciproqueThales[8][]{% % #1 Cl\'es % #2 NomTriangle + Points ABCEF pour droite (BC)//(EF) % #3 longueur AE % #4 longueur AB % #5 longueur AF % #6 longueur AC \StrMid{#2}{1}{1}[\NomA]\StrMid{#2}{2}{2}[\NomB]\StrMid{#2}{3}{3}[\NomC]\StrMid{#2}{4}{4}[\NomM]\StrMid{#2}{5}{5}[\NomN]% \ifboolKV[ClesThales]{FigureSeule}{% % \StrMid{#2}{1}{1}[\NomA]\StrMid{#2}{2}{2}[\NomB]\StrMid{#2}{3}{3}[\NomC]\StrMid{#2}{4}{4}[\NomM]\StrMid{#2}{5}{5}[\NomN]% \MPFigReciThales{\NomA}{\NomB}{\NomC}{\NomM}{\NomN}{\useKV[ClesThales]{Angle}}% }{\ifboolKV[ClesThales]{FigurecroiseeSeule}{% % \StrMid{#2}{1}{1}[\NomA]\StrMid{#2}{2}{2}[\NomB]\StrMid{#2}{3}{3}[\NomC]\StrMid{#2}{4}{4}[\NomM]\StrMid{#2}{5}{5}[\NomN]% \MPFigReciThalesCroisee{\NomA}{\NomB}{\NomC}{\NomM}{\NomN}{\useKV[ClesThales]{Angle}}% }{% \ifboolKV[ClesThales]{Figure}{% % \StrMid{#2}{1}{1}[\NomA]\StrMid{#2}{2}{2}[\NomB]\StrMid{#2}{3}{3}[\NomC]\StrMid{#2}{4}{4}[\NomM]\StrMid{#2}{5}{5}[\NomN]% \begin{multicols}{2} {\em La figure est donn\'ee \`a titre indicatif.} \[\MPFigReciThales{\NomA}{\NomB}{\NomC}{\NomM}{\NomN}{\useKV[ClesThales]{Angle}}\] \par\columnbreak\par \ReciThales[#1]{\StrMid{#2}{1}{1}}{\StrMid{#2}{2}{2}}{\StrMid{#2}{3}{3}}{\StrMid{#2}{4}{4}}{\StrMid{#2}{5}{5}}\par \ReciThalesCalculs[#1]{#2}{#3}{#4}{#5}{#6}{#7}{#8} \end{multicols} }{\ifboolKV[ClesThales]{Figurecroisee}{% % \StrMid{#2}{1}{1}[\NomA]\StrMid{#2}{2}{2}[\NomB]\StrMid{#2}{3}{3}[\NomC]\StrMid{#2}{4}{4}[\NomM]\StrMid{#2}{5}{5}[\NomN] \begin{minipage}{0.4\linewidth}% {\em La figure est donn\'ee \`a titre indicatif.}% \[\MPFigReciThalesCroisee{\NomA}{\NomB}{\NomC}{\NomM}{\NomN}{\useKV[ClesThales]{Angle}}\]% \end{minipage} \hfill \begin{minipage}{0.55\linewidth}% \ReciThales[#1]{\StrMid{#2}{1}{1}}{\StrMid{#2}{2}{2}}{\StrMid{#2}{3}{3}}{\StrMid{#2}{4}{4}}{\StrMid{#2}{5}{5}}\par \ReciThalesCalculs[#1]{#2}{#3}{#4}{#5}{#6}{#7}{#8}% \end{minipage}% }{\ReciThales[#1]{\StrMid{#2}{1}{1}}{\StrMid{#2}{2}{2}}{\StrMid{#2}{3}{3}}{\StrMid{#2}{4}{4}}{\StrMid{#2}{5}{5}}\par \ReciThalesCalculs[#1]{#2}{#3}{#4}{#5}{#6}{#7}{#8}% }% }% }% }% }% \newcommand\Thales[8][]{% \useKVdefault[ClesThales]% \setKV[ClesThales]{#1}% %Définir les points pour une utilisation perso \StrMid{#2}{1}{1}[\NomA]\StrMid{#2}{2}{2}[\NomB]\StrMid{#2}{3}{3}[\NomC]\StrMid{#2}{4}{4}[\NomM]\StrMid{#2}{5}{5}[\NomN]% \xdef\NomPointA{\NomA}% \xdef\NomPointB{\NomB}% \xdef\NomPointC{\NomC}% \xdef\NomTriangle{\NomA\NomB\NomC}% \xdef\NomPointM{\NomM}% \xdef\NomPointN{\NomN}% % \ifboolKV[ClesThales]{Reciproque}{% \ReciproqueThales[#1]{#2}{#3}{#4}{#5}{#6}{#7}{#8}% }{% \ifboolKV[ClesThales]{FigureSeule}{% \StrMid{#2}{1}{1}[\NomA]\StrMid{#2}{2}{2}[\NomB]\StrMid{#2}{3}{3}[\NomC]\StrMid{#2}{4}{4}[\NomM]\StrMid{#2}{5}{5}[\NomN]% \MPFigThales{\NomA}{\NomB}{\NomC}{\NomM}{\NomN}{\useKV[ClesThales]{Angle}}% }{% \ifboolKV[ClesThales]{FigurecroiseeSeule}{% \StrMid{#2}{1}{1}[\NomA]\StrMid{#2}{2}{2}[\NomB]\StrMid{#2}{3}{3}[\NomC]\StrMid{#2}{4}{4}[\NomM]\StrMid{#2}{5}{5}[\NomN]% \MPFigThalesCroisee{\NomA}{\NomB}{\NomC}{\NomM}{\NomN}{\useKV[ClesThales]{Angle}}% }{% \ifboolKV[ClesThales]{Redaction}{% \ifboolKV[ClesThales]{Figure}{% \StrMid{#2}{1}{1}[\NomA]\StrMid{#2}{2}{2}[\NomB]\StrMid{#2}{3}{3}[\NomC]\StrMid{#2}{4}{4}[\NomM]\StrMid{#2}{5}{5}[\NomN]% \begin{multicols}{2} {\em La figure est donn\'ee \`a titre indicatif.}% \[\MPFigThales{\NomA}{\NomB}{\NomC}{\NomM}{\NomN}{\useKV[ClesThales]{Angle}}\]% \par\columnbreak\par% \TTThales[#1]{\StrMid{#2}{1}{1}}{\StrMid{#2}{2}{2}}{\StrMid{#2}{3}{3}}{\StrMid{#2}{4}{4}}{\StrMid{#2}{5}{5}}% \end{multicols}% }{% \ifboolKV[ClesThales]{Figurecroisee}{% \StrMid{#2}{1}{1}[\NomA]\StrMid{#2}{2}{2}[\NomB]\StrMid{#2}{3}{3}[\NomC]\StrMid{#2}{4}{4}[\NomM]\StrMid{#2}{5}{5}[\NomN]% \begin{multicols}{2} {\em La figure est donn\'ee \`a titre indicatif.}% \[\MPFigThalesCroisee{\NomA}{\NomB}{\NomC}{\NomM}{\NomN}{\useKV[ClesThales]{Angle}}\]% \par\columnbreak\par% \TTThales[#1]{\StrMid{#2}{1}{1}}{\StrMid{#2}{2}{2}}{\StrMid{#2}{3}{3}}{\StrMid{#2}{4}{4}}{\StrMid{#2}{5}{5}}% \end{multicols} }{% \TTThales[#1]{\StrMid{#2}{1}{1}}{\StrMid{#2}{2}{2}}{\StrMid{#2}{3}{3}}{\StrMid{#2}{4}{4}}{\StrMid{#2}{5}{5}}% } } }{% \TThales[#1]{#2}{#3}{#4}{#5}{#6}{#7}{#8}% }% }% }% }% }%