%%%
% Thales
%%%
\def\filedateThales{2026/01/03}%
\def\fileversionThales{0.1c}%
\message{-- \filedateThales\space v\fileversionThales}%
%
\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,ModeleCouleur=5,CouleurNum={},CouleurDen={},ColumnBreak}%
%
\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
  \mplibforcehmode
  \begin{mplibcode}
    defaultcolormodel := \useKV[ClesThales]{ModeleCouleur};
    u:=\useKV[ClesThales]{Echelle};
    color CouleurNum,CouleurDen;
    \ifemptyKV[ClesThales]{CouleurNum}{CouleurNum=black;}{CouleurNum=\useKV[ClesThales]{CouleurNum};}%
    \ifemptyKV[ClesThales]{CouleurDen}{CouleurDen=black;}{CouleurDen=\useKV[ClesThales]{CouleurDen};}%
    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 CouleurDen<>black:
    draw triangle dashed evenly withpen pencircle scaled 1.5 withcolor CouleurDen;
    fi;
    if CouleurNum<>black:
    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}
}

%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
  \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}
}

%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
  \mplibforcehmode%
  \begin{mplibcode}
    defaultcolormodel := \useKV[ClesThales]{ModeleCouleur};
    u:=\useKV[ClesThales]{Echelle};
    color CouleurNum,CouleurDen;
    \ifemptyKV[ClesThales]{CouleurNum}{CouleurNum=black;}{CouleurNum=\useKV[ClesThales]{CouleurNum};}%
    \ifemptyKV[ClesThales]{CouleurDen}{CouleurDen=black;}{CouleurDen=\useKV[ClesThales]{CouleurDen};}%
    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 CouleurDen<>black:
    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 CouleurNum<>black:
    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
    pair K,L;
    K=1/2[B,C];
    L=2[O,K];
    label(TEX("$#1$"),I);
    label(TEX("$#2$"),1/4[B,L]);
    label(TEX("$#3$"),1/4[C,L]);
    label(TEX("$#4$"),1.1[B,M]);
    label(TEX("$#5$"),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);
    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}
}%

%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
  \mplibforcehmode%
  \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}
}

\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 :}%
      \[\frac{\ifboolKV[ClesThales]{Remediation}{\pointilles[1cm]}{\ifemptyKV[ClesThales]{CouleurNum}{#2#5}{\mathcolor{\useKV[ClesThales]{CouleurNum}}{#2#5}}}}{\ifboolKV[ClesThales]{Remediation}{\pointilles[1cm]}{\ifemptyKV[ClesThales]{CouleurDen}{#2#3}{\mathcolor{\useKV[ClesThales]{CouleurDen}}{#2#3}}}}=\frac{\ifboolKV[ClesThales]{Remediation}{\pointilles[1cm]}{\ifemptyKV[ClesThales]{CouleurNum}{#2#6}{\mathcolor{\useKV[ClesThales]{CouleurNum}}{#2#6}}}}{\ifboolKV[ClesThales]{Remediation}{\pointilles[1cm]}{\ifemptyKV[ClesThales]{CouleurDen}{#2#4}{\mathcolor{\useKV[ClesThales]{CouleurDen}}{#2#4}}}}=\frac{\ifboolKV[ClesThales]{Remediation}{\pointilles[1cm]}{\ifemptyKV[ClesThales]{CouleurNum}{#5#6}{\mathcolor{\useKV[ClesThales]{CouleurNum}}{#5#6}}}}{\ifboolKV[ClesThales]{Remediation}{\pointilles[1cm]}{\ifemptyKV[ClesThales]{CouleurDen}{#3#4}{\mathcolor{\useKV[ClesThales]{CouleurDen}}{#3#4}}}}.\]%
    }%
  }%
}%

\newcount\zzz\newcount\yyy\newcount\xxx%Pour se rappeller des calculs \`a faire et combien en faire%

\newcommand\TThalesCalculsD[8][]{%
  \setKV[ClesThales]{#1}%
  \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{#3*#7/#4}}%
        }{%
          \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{#3*#8/#5}}%
          }{}}{}
        }
      }{\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{#3*#8/#5}}%
          }{}}{}
      }
    }
  }{%
    \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{#6*#4/#7}}%
        }{%
          \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{#6*#5/#8}}%
            }{}}{}
        }
      }{\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{#6*#5/#8}}%
          }{}}{}
      }
    }{}
  }%
  % 
  \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{#4*#8/#5}}%
        }{%
          \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{#4*#6/#3}}%
            }{}}{}
        }
      }{\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{#4*#6/#3}}%
            }{}}{}
      }
    }
  }{%
    \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{#7*#5/#8}}%
        }{%
          \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{#7*#3/#6}}%
            }{}}{}
        }
      }{\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{#7*#3/#6}}%
            }{}}{}
      }}{}}%
  % 
  \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{#5*#7/#4}}%
        }{%
          \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{#5*#6/#3}}%
            }{}}{}
        }
      }{\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{#5*#6/#3}}%
            }{}}{}
      }
    }
  }{%
    \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{#8*#4/#7}}%
        }{%
          \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{#8*#3/#6}}%
            }{}}{}
        }
      }{\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{#8*#3/#6}}%
            }{}}{}
      }}{}
  }%
  %%
  \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{&}\xintifboolexpr{\fpeval{\ResultatThalesx-round(\ResultatThalesx,\useKV[ClesThales]{Precision},1)}==0}{=}{\approx}\SI{\fpeval{round(\ResultatThalesx,\useKV[ClesThales]{Precision},1)}}{\PfCThalesUnit}
    \fi
    %    % Deuxi\`eme compteur \yyy
    \ifnum\cmya>0
      \ifnum\cmxa=0
        %
      \else
        \uppercase{&}
      \fi
                     \Nomy\uppercase{&}\xintifboolexpr{\fpeval{\ResultatThalesy-round(\ResultatThalesy,\useKV[ClesThales]{Precision},1)}==0}{=}{\approx}\SI{\fpeval{round(\ResultatThalesy,\useKV[ClesThales]{Precision},1)}}{\PfCThalesUnit}
    \fi
%    %Troisi\`eme compteur \zzz
    \ifnum\cmza>0
      \ifnum\cmxa=0
        \ifnum\cmya=0                           
          %
        \else
          \uppercase{&}
        \fi
        \Nomz\uppercase{&}
      \else
        \uppercase{&}\Nomz\uppercase{&}
                                         \fi
                                         \xintifboolexpr{\fpeval{\ResultatThalesz-round(\ResultatThalesz,\useKV[ClesThales]{Precision},1)}==0}{=}{\approx}\SI{\fpeval{round(\ResultatThalesz,\useKV[ClesThales]{Precision},1)}}{\PfCThalesUnit}
    \fi
    \end{align*}
    }%
}{}%
}

\newcommand\TThalesCalculsE[8][]{%
  \setKV[ClesThales]{#1}%
  \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.}%
          \[\MPFigThales{\NomA}{\NomB}{\NomC}{\NomM}{\NomN}{\useKV[ClesThales]{Angle}}\]%
          \ifboolKV[ClesThales]{ColumnBreak}{\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.}%
            \[\MPFigThalesCroisee{\NomA}{\NomB}{\NomC}{\NomM}{\NomN}{\useKV[ClesThales]{Angle}}\]%
            \ifboolKV[ClesThales]{ColumnBreak}{\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&#2#6\\
        \hline
        #2#3&#2#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.}
          \[\MPFigReciThales{\NomA}{\NomB}{\NomC}{\NomM}{\NomN}{\useKV[ClesThales]{Angle}}\]
          \ifboolKV[ClesThales]{ColumnBreak}{\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.}%
              \[\MPFigThales{\NomA}{\NomB}{\NomC}{\NomM}{\NomN}{\useKV[ClesThales]{Angle}}\]%
              \ifboolKV[ClesThales]{ColumnBreak}{\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.}%
                \[\MPFigThalesCroisee{\NomA}{\NomB}{\NomC}{\NomM}{\NomN}{\useKV[ClesThales]{Angle}}\]%
                \ifboolKV[ClesThales]{ColumnBreak}{\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}%
        }%
      }%
    }%
  }%
}%

\makeatletter
\NewDocumentCommand\NThales{om}{%
  \PfC@Thales@i#2\@nil%
  \Thales[#1]{\PfC@NomTriangle}{\PfCValeuraa}{\PfCValeurab}{\PfCValeurac}{\PfCValeurba}{\PfCValeurbb}{\PfCValeurbc}%
}%

\def\PfC@Thales@i#1#2#3,#4#5,{%
  \edef\PfC@NomTriangle{{#1}{#2}{#3}{#4}{#5}}%
  \PfC@Thales@iii%
}%

\def\PfC@Thales@iii#1/#2=#3/#4=#5/#6\@nil{%
  \edef\PfCValeuraa{#1}%
  \edef\PfCValeurba{#2}%
  \edef\PfCValeurab{#3}%
  \edef\PfCValeurbb{#4}%
  \edef\PfCValeurac{#5}%
  \edef\PfCValeurbc{#6}%
}%
\makeatother