Tick Marks in Geometry












2














Here is an excerpt from my code:



begin{tikzpicture}[scale=5.5]
coordinate[label=left:$A$] (A) at (0,0);
coordinate[label=right:$B$] (B) at (1,0);
coordinate[label=:$C$] (C) at (0.5,0.866);
draw (A)--(B)--(C)--(A);
end{tikzpicture}


I want to denote AB=BC using the tick mark notation. Also, point C isn't exactly where it should be. How can I fix that? I rounded sqrt(3)/2 to 0.866.










share|improve this question







New contributor




M. C. is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
















  • 3




    Welcome to TeX.SE! Please show us -- as usual here --an short compilable code resulting in your issue ...
    – Kurt
    2 days ago






  • 3




    It would also be helpful if you could include a sketch of how the output should look like.
    – samcarter
    2 days ago










  • TikZ understands polar coordinates such as coordinate[label=:$C$] (C) at (60:1); It also understands coordinate[label=:$C$] (C) at (0.5,{sqrt(3)/2});.
    – marmot
    2 days ago
















2














Here is an excerpt from my code:



begin{tikzpicture}[scale=5.5]
coordinate[label=left:$A$] (A) at (0,0);
coordinate[label=right:$B$] (B) at (1,0);
coordinate[label=:$C$] (C) at (0.5,0.866);
draw (A)--(B)--(C)--(A);
end{tikzpicture}


I want to denote AB=BC using the tick mark notation. Also, point C isn't exactly where it should be. How can I fix that? I rounded sqrt(3)/2 to 0.866.










share|improve this question







New contributor




M. C. is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
















  • 3




    Welcome to TeX.SE! Please show us -- as usual here --an short compilable code resulting in your issue ...
    – Kurt
    2 days ago






  • 3




    It would also be helpful if you could include a sketch of how the output should look like.
    – samcarter
    2 days ago










  • TikZ understands polar coordinates such as coordinate[label=:$C$] (C) at (60:1); It also understands coordinate[label=:$C$] (C) at (0.5,{sqrt(3)/2});.
    – marmot
    2 days ago














2












2








2


0





Here is an excerpt from my code:



begin{tikzpicture}[scale=5.5]
coordinate[label=left:$A$] (A) at (0,0);
coordinate[label=right:$B$] (B) at (1,0);
coordinate[label=:$C$] (C) at (0.5,0.866);
draw (A)--(B)--(C)--(A);
end{tikzpicture}


I want to denote AB=BC using the tick mark notation. Also, point C isn't exactly where it should be. How can I fix that? I rounded sqrt(3)/2 to 0.866.










share|improve this question







New contributor




M. C. is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.











Here is an excerpt from my code:



begin{tikzpicture}[scale=5.5]
coordinate[label=left:$A$] (A) at (0,0);
coordinate[label=right:$B$] (B) at (1,0);
coordinate[label=:$C$] (C) at (0.5,0.866);
draw (A)--(B)--(C)--(A);
end{tikzpicture}


I want to denote AB=BC using the tick mark notation. Also, point C isn't exactly where it should be. How can I fix that? I rounded sqrt(3)/2 to 0.866.







graphs






share|improve this question







New contributor




M. C. is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.











share|improve this question







New contributor




M. C. is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.









share|improve this question




share|improve this question






New contributor




M. C. is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.









asked 2 days ago









M. C.M. C.

112




112




New contributor




M. C. is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.





New contributor





M. C. is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.






M. C. is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.








  • 3




    Welcome to TeX.SE! Please show us -- as usual here --an short compilable code resulting in your issue ...
    – Kurt
    2 days ago






  • 3




    It would also be helpful if you could include a sketch of how the output should look like.
    – samcarter
    2 days ago










  • TikZ understands polar coordinates such as coordinate[label=:$C$] (C) at (60:1); It also understands coordinate[label=:$C$] (C) at (0.5,{sqrt(3)/2});.
    – marmot
    2 days ago














  • 3




    Welcome to TeX.SE! Please show us -- as usual here --an short compilable code resulting in your issue ...
    – Kurt
    2 days ago






  • 3




    It would also be helpful if you could include a sketch of how the output should look like.
    – samcarter
    2 days ago










  • TikZ understands polar coordinates such as coordinate[label=:$C$] (C) at (60:1); It also understands coordinate[label=:$C$] (C) at (0.5,{sqrt(3)/2});.
    – marmot
    2 days ago








3




3




Welcome to TeX.SE! Please show us -- as usual here --an short compilable code resulting in your issue ...
– Kurt
2 days ago




Welcome to TeX.SE! Please show us -- as usual here --an short compilable code resulting in your issue ...
– Kurt
2 days ago




3




3




It would also be helpful if you could include a sketch of how the output should look like.
– samcarter
2 days ago




It would also be helpful if you could include a sketch of how the output should look like.
– samcarter
2 days ago












TikZ understands polar coordinates such as coordinate[label=:$C$] (C) at (60:1); It also understands coordinate[label=:$C$] (C) at (0.5,{sqrt(3)/2});.
– marmot
2 days ago




TikZ understands polar coordinates such as coordinate[label=:$C$] (C) at (60:1); It also understands coordinate[label=:$C$] (C) at (0.5,{sqrt(3)/2});.
– marmot
2 days ago










3 Answers
3






active

oldest

votes


















3














A PSTricks solution just for fun purposes.



documentclass[pstricks,12pt,border=1cm]{standalone}
usepackage{pst-eucl}
begin{document}
pspicture[MarkAngle=90](-4,4)
pstTriangle(4;150){C}(-4,0){A}(0,0){B}
pstSegmentMark{A}{B}
pstSegmentMark{B}{C}
endpspicture
end{document}


enter image description here



Bonus



documentclass[pstricks,12pt,border=1cm]{standalone}
usepackage{pst-eucl}
begin{document}
foreach i in {90,100,...,170}{%
pspicture[MarkAngle=90](-4,4)
pstTriangle(4;i){C}(-4,0){A}(0,0){B}
pstSegmentMark{A}{B}
pstSegmentMark{B}{C}
endpspicture}
end{document}


enter image description here






share|improve this answer































    3














    one more tikz solution. for marks are used math symbol | in nodes with option sloped placed on lines:



    documentclass[tikz,border=3.141592mm]{standalone}

    begin{document}
    begin{tikzpicture}[scale=5.5]
    coordinate[label=left:$A$] (A) at (0,0);
    coordinate[label=right:$B$] (B) at (1,0);
    coordinate[label=$C$] (C) at (0.5,0.866);
    draw (A) -- node {$|$} (B) -- node[sloped] {$|$} (C) -- (A);
    end{tikzpicture}
    end{document}


    now tikz version 3.1 in miktex works ...



    enter image description here






    share|improve this answer























    • The mark on BC is not perpendicular I think ( I compile with my heart).
      – God Must Be Crazy
      yesterday






    • 1




      @GodMustBeCrazy, of course not, i forgot to add option sloped ... i correct this.
      – Zarko
      yesterday



















    2














    Welcome to TeX.SE! You can add these marks with decorations.markings. Since you want two of them, it is shorter to use the .list key for that. Further, TikZ understands polar coordinates, and it also understands (0.5,{sqrt(3)/2}), so there is no need to unbury your calculator. ;-)



    documentclass[tikz,border=3.14mm]{standalone}
    usetikzlibrary{decorations.markings}
    begin{document}
    begin{tikzpicture}[scale=5.5,equal mark/.style={postaction={decorate,
    decoration={markings,mark=at position #1 with {draw (-2pt,-4pt) -- (-2pt,4pt);
    draw (2pt,-4pt) -- (2pt,4pt);}}}}]
    coordinate[label=left:$A$] (A) at (0,0);
    coordinate[label=right:$B$] (B) at (1,0);
    coordinate[label=:$C$] (C) at (60:1);
    draw[equal mark/.list={1/6,1/2}] (A)--(B)--(C)--cycle;
    end{tikzpicture}
    end{document}


    enter image description here



    As you can see, this code starts with documentclass and ends with end{document}, and is compilable. Kurt asked you in his comment to add such a code.



    And you may simplify/shorten the code using a foreach loop.



    documentclass[tikz,border=3.14mm]{standalone}
    usetikzlibrary{decorations.markings}
    begin{document}
    begin{tikzpicture}[scale=5.5,equal mark/.style={postaction={decorate,
    decoration={markings,mark=at position #1 with {draw (-2pt,-4pt) -- (-2pt,4pt);
    draw (2pt,-4pt) -- (2pt,4pt);}}}}]
    foreach X/Y in {210/A,-30/B,90/C}
    {coordinate[label=X:$Y$] (Y) at (X:{1/sqrt(3)});}
    draw[equal mark/.list={1/6,1/2,5/6}] (A)--(B)--(C)--cycle;
    end{tikzpicture}
    end{document}





    share|improve this answer























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      3 Answers
      3






      active

      oldest

      votes








      3 Answers
      3






      active

      oldest

      votes









      active

      oldest

      votes






      active

      oldest

      votes









      3














      A PSTricks solution just for fun purposes.



      documentclass[pstricks,12pt,border=1cm]{standalone}
      usepackage{pst-eucl}
      begin{document}
      pspicture[MarkAngle=90](-4,4)
      pstTriangle(4;150){C}(-4,0){A}(0,0){B}
      pstSegmentMark{A}{B}
      pstSegmentMark{B}{C}
      endpspicture
      end{document}


      enter image description here



      Bonus



      documentclass[pstricks,12pt,border=1cm]{standalone}
      usepackage{pst-eucl}
      begin{document}
      foreach i in {90,100,...,170}{%
      pspicture[MarkAngle=90](-4,4)
      pstTriangle(4;i){C}(-4,0){A}(0,0){B}
      pstSegmentMark{A}{B}
      pstSegmentMark{B}{C}
      endpspicture}
      end{document}


      enter image description here






      share|improve this answer




























        3














        A PSTricks solution just for fun purposes.



        documentclass[pstricks,12pt,border=1cm]{standalone}
        usepackage{pst-eucl}
        begin{document}
        pspicture[MarkAngle=90](-4,4)
        pstTriangle(4;150){C}(-4,0){A}(0,0){B}
        pstSegmentMark{A}{B}
        pstSegmentMark{B}{C}
        endpspicture
        end{document}


        enter image description here



        Bonus



        documentclass[pstricks,12pt,border=1cm]{standalone}
        usepackage{pst-eucl}
        begin{document}
        foreach i in {90,100,...,170}{%
        pspicture[MarkAngle=90](-4,4)
        pstTriangle(4;i){C}(-4,0){A}(0,0){B}
        pstSegmentMark{A}{B}
        pstSegmentMark{B}{C}
        endpspicture}
        end{document}


        enter image description here






        share|improve this answer


























          3












          3








          3






          A PSTricks solution just for fun purposes.



          documentclass[pstricks,12pt,border=1cm]{standalone}
          usepackage{pst-eucl}
          begin{document}
          pspicture[MarkAngle=90](-4,4)
          pstTriangle(4;150){C}(-4,0){A}(0,0){B}
          pstSegmentMark{A}{B}
          pstSegmentMark{B}{C}
          endpspicture
          end{document}


          enter image description here



          Bonus



          documentclass[pstricks,12pt,border=1cm]{standalone}
          usepackage{pst-eucl}
          begin{document}
          foreach i in {90,100,...,170}{%
          pspicture[MarkAngle=90](-4,4)
          pstTriangle(4;i){C}(-4,0){A}(0,0){B}
          pstSegmentMark{A}{B}
          pstSegmentMark{B}{C}
          endpspicture}
          end{document}


          enter image description here






          share|improve this answer














          A PSTricks solution just for fun purposes.



          documentclass[pstricks,12pt,border=1cm]{standalone}
          usepackage{pst-eucl}
          begin{document}
          pspicture[MarkAngle=90](-4,4)
          pstTriangle(4;150){C}(-4,0){A}(0,0){B}
          pstSegmentMark{A}{B}
          pstSegmentMark{B}{C}
          endpspicture
          end{document}


          enter image description here



          Bonus



          documentclass[pstricks,12pt,border=1cm]{standalone}
          usepackage{pst-eucl}
          begin{document}
          foreach i in {90,100,...,170}{%
          pspicture[MarkAngle=90](-4,4)
          pstTriangle(4;i){C}(-4,0){A}(0,0){B}
          pstSegmentMark{A}{B}
          pstSegmentMark{B}{C}
          endpspicture}
          end{document}


          enter image description here







          share|improve this answer














          share|improve this answer



          share|improve this answer








          edited yesterday

























          answered yesterday









          God Must Be CrazyGod Must Be Crazy

          6,00511039




          6,00511039























              3














              one more tikz solution. for marks are used math symbol | in nodes with option sloped placed on lines:



              documentclass[tikz,border=3.141592mm]{standalone}

              begin{document}
              begin{tikzpicture}[scale=5.5]
              coordinate[label=left:$A$] (A) at (0,0);
              coordinate[label=right:$B$] (B) at (1,0);
              coordinate[label=$C$] (C) at (0.5,0.866);
              draw (A) -- node {$|$} (B) -- node[sloped] {$|$} (C) -- (A);
              end{tikzpicture}
              end{document}


              now tikz version 3.1 in miktex works ...



              enter image description here






              share|improve this answer























              • The mark on BC is not perpendicular I think ( I compile with my heart).
                – God Must Be Crazy
                yesterday






              • 1




                @GodMustBeCrazy, of course not, i forgot to add option sloped ... i correct this.
                – Zarko
                yesterday
















              3














              one more tikz solution. for marks are used math symbol | in nodes with option sloped placed on lines:



              documentclass[tikz,border=3.141592mm]{standalone}

              begin{document}
              begin{tikzpicture}[scale=5.5]
              coordinate[label=left:$A$] (A) at (0,0);
              coordinate[label=right:$B$] (B) at (1,0);
              coordinate[label=$C$] (C) at (0.5,0.866);
              draw (A) -- node {$|$} (B) -- node[sloped] {$|$} (C) -- (A);
              end{tikzpicture}
              end{document}


              now tikz version 3.1 in miktex works ...



              enter image description here






              share|improve this answer























              • The mark on BC is not perpendicular I think ( I compile with my heart).
                – God Must Be Crazy
                yesterday






              • 1




                @GodMustBeCrazy, of course not, i forgot to add option sloped ... i correct this.
                – Zarko
                yesterday














              3












              3








              3






              one more tikz solution. for marks are used math symbol | in nodes with option sloped placed on lines:



              documentclass[tikz,border=3.141592mm]{standalone}

              begin{document}
              begin{tikzpicture}[scale=5.5]
              coordinate[label=left:$A$] (A) at (0,0);
              coordinate[label=right:$B$] (B) at (1,0);
              coordinate[label=$C$] (C) at (0.5,0.866);
              draw (A) -- node {$|$} (B) -- node[sloped] {$|$} (C) -- (A);
              end{tikzpicture}
              end{document}


              now tikz version 3.1 in miktex works ...



              enter image description here






              share|improve this answer














              one more tikz solution. for marks are used math symbol | in nodes with option sloped placed on lines:



              documentclass[tikz,border=3.141592mm]{standalone}

              begin{document}
              begin{tikzpicture}[scale=5.5]
              coordinate[label=left:$A$] (A) at (0,0);
              coordinate[label=right:$B$] (B) at (1,0);
              coordinate[label=$C$] (C) at (0.5,0.866);
              draw (A) -- node {$|$} (B) -- node[sloped] {$|$} (C) -- (A);
              end{tikzpicture}
              end{document}


              now tikz version 3.1 in miktex works ...



              enter image description here







              share|improve this answer














              share|improve this answer



              share|improve this answer








              edited yesterday

























              answered yesterday









              ZarkoZarko

              122k865158




              122k865158












              • The mark on BC is not perpendicular I think ( I compile with my heart).
                – God Must Be Crazy
                yesterday






              • 1




                @GodMustBeCrazy, of course not, i forgot to add option sloped ... i correct this.
                – Zarko
                yesterday


















              • The mark on BC is not perpendicular I think ( I compile with my heart).
                – God Must Be Crazy
                yesterday






              • 1




                @GodMustBeCrazy, of course not, i forgot to add option sloped ... i correct this.
                – Zarko
                yesterday
















              The mark on BC is not perpendicular I think ( I compile with my heart).
              – God Must Be Crazy
              yesterday




              The mark on BC is not perpendicular I think ( I compile with my heart).
              – God Must Be Crazy
              yesterday




              1




              1




              @GodMustBeCrazy, of course not, i forgot to add option sloped ... i correct this.
              – Zarko
              yesterday




              @GodMustBeCrazy, of course not, i forgot to add option sloped ... i correct this.
              – Zarko
              yesterday











              2














              Welcome to TeX.SE! You can add these marks with decorations.markings. Since you want two of them, it is shorter to use the .list key for that. Further, TikZ understands polar coordinates, and it also understands (0.5,{sqrt(3)/2}), so there is no need to unbury your calculator. ;-)



              documentclass[tikz,border=3.14mm]{standalone}
              usetikzlibrary{decorations.markings}
              begin{document}
              begin{tikzpicture}[scale=5.5,equal mark/.style={postaction={decorate,
              decoration={markings,mark=at position #1 with {draw (-2pt,-4pt) -- (-2pt,4pt);
              draw (2pt,-4pt) -- (2pt,4pt);}}}}]
              coordinate[label=left:$A$] (A) at (0,0);
              coordinate[label=right:$B$] (B) at (1,0);
              coordinate[label=:$C$] (C) at (60:1);
              draw[equal mark/.list={1/6,1/2}] (A)--(B)--(C)--cycle;
              end{tikzpicture}
              end{document}


              enter image description here



              As you can see, this code starts with documentclass and ends with end{document}, and is compilable. Kurt asked you in his comment to add such a code.



              And you may simplify/shorten the code using a foreach loop.



              documentclass[tikz,border=3.14mm]{standalone}
              usetikzlibrary{decorations.markings}
              begin{document}
              begin{tikzpicture}[scale=5.5,equal mark/.style={postaction={decorate,
              decoration={markings,mark=at position #1 with {draw (-2pt,-4pt) -- (-2pt,4pt);
              draw (2pt,-4pt) -- (2pt,4pt);}}}}]
              foreach X/Y in {210/A,-30/B,90/C}
              {coordinate[label=X:$Y$] (Y) at (X:{1/sqrt(3)});}
              draw[equal mark/.list={1/6,1/2,5/6}] (A)--(B)--(C)--cycle;
              end{tikzpicture}
              end{document}





              share|improve this answer




























                2














                Welcome to TeX.SE! You can add these marks with decorations.markings. Since you want two of them, it is shorter to use the .list key for that. Further, TikZ understands polar coordinates, and it also understands (0.5,{sqrt(3)/2}), so there is no need to unbury your calculator. ;-)



                documentclass[tikz,border=3.14mm]{standalone}
                usetikzlibrary{decorations.markings}
                begin{document}
                begin{tikzpicture}[scale=5.5,equal mark/.style={postaction={decorate,
                decoration={markings,mark=at position #1 with {draw (-2pt,-4pt) -- (-2pt,4pt);
                draw (2pt,-4pt) -- (2pt,4pt);}}}}]
                coordinate[label=left:$A$] (A) at (0,0);
                coordinate[label=right:$B$] (B) at (1,0);
                coordinate[label=:$C$] (C) at (60:1);
                draw[equal mark/.list={1/6,1/2}] (A)--(B)--(C)--cycle;
                end{tikzpicture}
                end{document}


                enter image description here



                As you can see, this code starts with documentclass and ends with end{document}, and is compilable. Kurt asked you in his comment to add such a code.



                And you may simplify/shorten the code using a foreach loop.



                documentclass[tikz,border=3.14mm]{standalone}
                usetikzlibrary{decorations.markings}
                begin{document}
                begin{tikzpicture}[scale=5.5,equal mark/.style={postaction={decorate,
                decoration={markings,mark=at position #1 with {draw (-2pt,-4pt) -- (-2pt,4pt);
                draw (2pt,-4pt) -- (2pt,4pt);}}}}]
                foreach X/Y in {210/A,-30/B,90/C}
                {coordinate[label=X:$Y$] (Y) at (X:{1/sqrt(3)});}
                draw[equal mark/.list={1/6,1/2,5/6}] (A)--(B)--(C)--cycle;
                end{tikzpicture}
                end{document}





                share|improve this answer


























                  2












                  2








                  2






                  Welcome to TeX.SE! You can add these marks with decorations.markings. Since you want two of them, it is shorter to use the .list key for that. Further, TikZ understands polar coordinates, and it also understands (0.5,{sqrt(3)/2}), so there is no need to unbury your calculator. ;-)



                  documentclass[tikz,border=3.14mm]{standalone}
                  usetikzlibrary{decorations.markings}
                  begin{document}
                  begin{tikzpicture}[scale=5.5,equal mark/.style={postaction={decorate,
                  decoration={markings,mark=at position #1 with {draw (-2pt,-4pt) -- (-2pt,4pt);
                  draw (2pt,-4pt) -- (2pt,4pt);}}}}]
                  coordinate[label=left:$A$] (A) at (0,0);
                  coordinate[label=right:$B$] (B) at (1,0);
                  coordinate[label=:$C$] (C) at (60:1);
                  draw[equal mark/.list={1/6,1/2}] (A)--(B)--(C)--cycle;
                  end{tikzpicture}
                  end{document}


                  enter image description here



                  As you can see, this code starts with documentclass and ends with end{document}, and is compilable. Kurt asked you in his comment to add such a code.



                  And you may simplify/shorten the code using a foreach loop.



                  documentclass[tikz,border=3.14mm]{standalone}
                  usetikzlibrary{decorations.markings}
                  begin{document}
                  begin{tikzpicture}[scale=5.5,equal mark/.style={postaction={decorate,
                  decoration={markings,mark=at position #1 with {draw (-2pt,-4pt) -- (-2pt,4pt);
                  draw (2pt,-4pt) -- (2pt,4pt);}}}}]
                  foreach X/Y in {210/A,-30/B,90/C}
                  {coordinate[label=X:$Y$] (Y) at (X:{1/sqrt(3)});}
                  draw[equal mark/.list={1/6,1/2,5/6}] (A)--(B)--(C)--cycle;
                  end{tikzpicture}
                  end{document}





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                  Welcome to TeX.SE! You can add these marks with decorations.markings. Since you want two of them, it is shorter to use the .list key for that. Further, TikZ understands polar coordinates, and it also understands (0.5,{sqrt(3)/2}), so there is no need to unbury your calculator. ;-)



                  documentclass[tikz,border=3.14mm]{standalone}
                  usetikzlibrary{decorations.markings}
                  begin{document}
                  begin{tikzpicture}[scale=5.5,equal mark/.style={postaction={decorate,
                  decoration={markings,mark=at position #1 with {draw (-2pt,-4pt) -- (-2pt,4pt);
                  draw (2pt,-4pt) -- (2pt,4pt);}}}}]
                  coordinate[label=left:$A$] (A) at (0,0);
                  coordinate[label=right:$B$] (B) at (1,0);
                  coordinate[label=:$C$] (C) at (60:1);
                  draw[equal mark/.list={1/6,1/2}] (A)--(B)--(C)--cycle;
                  end{tikzpicture}
                  end{document}


                  enter image description here



                  As you can see, this code starts with documentclass and ends with end{document}, and is compilable. Kurt asked you in his comment to add such a code.



                  And you may simplify/shorten the code using a foreach loop.



                  documentclass[tikz,border=3.14mm]{standalone}
                  usetikzlibrary{decorations.markings}
                  begin{document}
                  begin{tikzpicture}[scale=5.5,equal mark/.style={postaction={decorate,
                  decoration={markings,mark=at position #1 with {draw (-2pt,-4pt) -- (-2pt,4pt);
                  draw (2pt,-4pt) -- (2pt,4pt);}}}}]
                  foreach X/Y in {210/A,-30/B,90/C}
                  {coordinate[label=X:$Y$] (Y) at (X:{1/sqrt(3)});}
                  draw[equal mark/.list={1/6,1/2,5/6}] (A)--(B)--(C)--cycle;
                  end{tikzpicture}
                  end{document}






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                  marmotmarmot

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