Line passing through a point and parallel to another: Where am I wrong?












2














documentclass{standalone}
usepackage{tikz}
usetikzlibrary{intersections}
usetikzlibrary{calc}
begin{document}

begin{tikzpicture}

coordinate (A) at (0,0);
coordinate (B) at (2,4);
coordinate (C) at (8,0);
coordinate (M) at (4,0);

path[name path=Circle] (B) circle [radius=3cm];
path[name path=AB] (A)--(B);
path[name path=BC] (B)--(C);
path [name intersections={of=Circle and BC}];
coordinate (E) at (intersection-1);
path [name intersections={of=Circle and AB}];
coordinate (D) at (intersection-1);

draw[thick](A)--(B)--(C)--cycle;
draw[thick](B) circle [radius=3cm];
draw[thick](D)--(E) (M)--(B);

% From a point draw a parallel line by calculating the vector
coordinate (P) at (intersection cs:first line={(B)--(C)}, second line={(A) -- +($(E)-(D)$)});

% Here is my problem:
coordinate (N) at (intersection cs:first line={(B)--(M)}, second line={(C) -- +($(D)-(E)$)});

draw[thick, red] (A)--(P) (C)--(N);

end{tikzpicture}
end{document}


Question: The second drawn line, which is supposed to also be a parallel, is not. What am I doing wrong?



enter image description here










share|improve this question



























    2














    documentclass{standalone}
    usepackage{tikz}
    usetikzlibrary{intersections}
    usetikzlibrary{calc}
    begin{document}

    begin{tikzpicture}

    coordinate (A) at (0,0);
    coordinate (B) at (2,4);
    coordinate (C) at (8,0);
    coordinate (M) at (4,0);

    path[name path=Circle] (B) circle [radius=3cm];
    path[name path=AB] (A)--(B);
    path[name path=BC] (B)--(C);
    path [name intersections={of=Circle and BC}];
    coordinate (E) at (intersection-1);
    path [name intersections={of=Circle and AB}];
    coordinate (D) at (intersection-1);

    draw[thick](A)--(B)--(C)--cycle;
    draw[thick](B) circle [radius=3cm];
    draw[thick](D)--(E) (M)--(B);

    % From a point draw a parallel line by calculating the vector
    coordinate (P) at (intersection cs:first line={(B)--(C)}, second line={(A) -- +($(E)-(D)$)});

    % Here is my problem:
    coordinate (N) at (intersection cs:first line={(B)--(M)}, second line={(C) -- +($(D)-(E)$)});

    draw[thick, red] (A)--(P) (C)--(N);

    end{tikzpicture}
    end{document}


    Question: The second drawn line, which is supposed to also be a parallel, is not. What am I doing wrong?



    enter image description here










    share|improve this question

























      2












      2








      2







      documentclass{standalone}
      usepackage{tikz}
      usetikzlibrary{intersections}
      usetikzlibrary{calc}
      begin{document}

      begin{tikzpicture}

      coordinate (A) at (0,0);
      coordinate (B) at (2,4);
      coordinate (C) at (8,0);
      coordinate (M) at (4,0);

      path[name path=Circle] (B) circle [radius=3cm];
      path[name path=AB] (A)--(B);
      path[name path=BC] (B)--(C);
      path [name intersections={of=Circle and BC}];
      coordinate (E) at (intersection-1);
      path [name intersections={of=Circle and AB}];
      coordinate (D) at (intersection-1);

      draw[thick](A)--(B)--(C)--cycle;
      draw[thick](B) circle [radius=3cm];
      draw[thick](D)--(E) (M)--(B);

      % From a point draw a parallel line by calculating the vector
      coordinate (P) at (intersection cs:first line={(B)--(C)}, second line={(A) -- +($(E)-(D)$)});

      % Here is my problem:
      coordinate (N) at (intersection cs:first line={(B)--(M)}, second line={(C) -- +($(D)-(E)$)});

      draw[thick, red] (A)--(P) (C)--(N);

      end{tikzpicture}
      end{document}


      Question: The second drawn line, which is supposed to also be a parallel, is not. What am I doing wrong?



      enter image description here










      share|improve this question













      documentclass{standalone}
      usepackage{tikz}
      usetikzlibrary{intersections}
      usetikzlibrary{calc}
      begin{document}

      begin{tikzpicture}

      coordinate (A) at (0,0);
      coordinate (B) at (2,4);
      coordinate (C) at (8,0);
      coordinate (M) at (4,0);

      path[name path=Circle] (B) circle [radius=3cm];
      path[name path=AB] (A)--(B);
      path[name path=BC] (B)--(C);
      path [name intersections={of=Circle and BC}];
      coordinate (E) at (intersection-1);
      path [name intersections={of=Circle and AB}];
      coordinate (D) at (intersection-1);

      draw[thick](A)--(B)--(C)--cycle;
      draw[thick](B) circle [radius=3cm];
      draw[thick](D)--(E) (M)--(B);

      % From a point draw a parallel line by calculating the vector
      coordinate (P) at (intersection cs:first line={(B)--(C)}, second line={(A) -- +($(E)-(D)$)});

      % Here is my problem:
      coordinate (N) at (intersection cs:first line={(B)--(M)}, second line={(C) -- +($(D)-(E)$)});

      draw[thick, red] (A)--(P) (C)--(N);

      end{tikzpicture}
      end{document}


      Question: The second drawn line, which is supposed to also be a parallel, is not. What am I doing wrong?



      enter image description here







      tikz-pgf






      share|improve this question













      share|improve this question











      share|improve this question




      share|improve this question










      asked 53 mins ago









      blackened

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          2 Answers
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          oldest

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          2














          If you use the + syntax in this context, it seems not to always give you what one may expect. In general, + means "relative to the first coordinate of this path". But who knows what the first coordinate is in the context of intersection cs:? It is, however, not too difficult to produce the parallel lines just by computing the slope and using it. For the sake of clarity, I labeled all coordinates.



          documentclass{standalone}
          usepackage{tikz}
          usetikzlibrary{intersections}
          usetikzlibrary{calc}
          begin{document}

          begin{tikzpicture}

          coordinate[label=left:$A$] (A) at (0,0);
          coordinate[label=above:$B$] (B) at (2,4);
          coordinate[label=right:$C$] (C) at (8,0);
          coordinate[label=45:$M$] (M) at (4,0);

          draw[name path=Circle] (B) circle [radius=3cm];
          path[name path=AB] (A)--(B);
          path[name path=BC] (B)--(C);
          path [name intersections={of=Circle and BC}];
          coordinate[label=right:$E$] (E) at (intersection-1);
          path [name intersections={of=Circle and AB}];
          coordinate[label=left:$D$] (D) at (intersection-1);

          draw[thick](A)--(B)--(C)--cycle;
          %draw[thick](B) circle [radius=3cm];
          draw[thick](D)--(E) (M)--(B);

          % From a point draw a parallel line by calculating the vector
          path let p1=($(E)-(D)$),n1={atan2(y1,x1)} in
          ($(A)+(n1:1)$) coordinate (auxA)
          ($(C)+(n1:1)$) coordinate (auxC);
          coordinate[label=right:$P$] (P) at (intersection cs:first line={(B)--(C)},
          second line={(A) -- (auxA)});

          % Here is my problem:
          coordinate[label=below:$N$]
          (N) at (intersection cs:first line={(B)--(M)},
          second line={(C) -- (auxC)});

          draw[thick, red] (A)--(P) (C)--(N) ;

          end{tikzpicture}
          end{document}


          enter image description here



          As you see, the red lines are parallel.



          One may want cast this into a style:

          documentclass{standalone}
          usepackage{tikz}
          usetikzlibrary{intersections}
          usetikzlibrary{calc}
          begin{document}
          tikzset{line through/.style args={#1 parallel to line through #2 and #3 and
          length #4}{insert path={%
          let p1=($(#3)-(#2)$),n1={atan2(y1,x1)} in (#1) -- ++ (n1:#4)}}}
          begin{tikzpicture}

          coordinate[label=left:$A$] (A) at (0,0);
          coordinate[label=above:$B$] (B) at (2,4);
          coordinate[label=right:$C$] (C) at (8,0);
          coordinate[label=45:$M$] (M) at (4,0);

          draw[name path=Circle] (B) circle [radius=3cm];
          path[name path=AB] (A)--(B);
          path[name path=BC] (B)--(C);
          path [name intersections={of=Circle and BC}];
          coordinate[label=right:$E$] (E) at (intersection-1);
          path [name intersections={of=Circle and AB}];
          coordinate[label=left:$D$] (D) at (intersection-1);

          draw[thick](A)--(B)--(C)--cycle;
          %draw[thick](B) circle [radius=3cm];
          draw[thick](D)--(E) (M)--(B);

          % From a point draw a parallel line by calculating the vector
          path[line through=A parallel to line through E and D and length 1]
          coordinate (auxA)
          [line through=C parallel to line through E and D and length 1]
          coordinate (auxC);

          coordinate[label=right:$P$] (P) at (intersection cs:first line={(B)--(C)},
          second line={(A) -- (auxA)});

          % Here is my problem:
          coordinate[label=below:$N$]
          (N) at (intersection cs:first line={(B)--(M)},
          second line={(C) -- (auxC)});

          draw[thick, red] (A)--(P) (C)--(N) ;

          end{tikzpicture}
          end{document}





          share|improve this answer























          • Thank you. I was following this answer.
            – blackened
            27 mins ago












          • @blackened Yes, there it is very clear what the first point of the path is. Therefore, it is clear what + does. However, in the context of intersection cs: it is not clear to me where single paths start and end, and hence -- +(coordinate) may not be what one may thing it is. I am sorry if you feel that my wording is offensive, would like to apologize, and change it right away.
            – marmot
            25 mins ago












          • No worries at all. I just assumed that that answer encompassed all cases. How can I turn your approach to a tikz style definition?
            – blackened
            23 mins ago










          • @blackened What precisely do you want the style to accomplish? A line through a given point with the slope coinciding with the one of another line. (And rereading my original post I think my wording did indeed not reflect what I wanted to say.)
            – marmot
            20 mins ago










          • What precisely do you want the style to accomplish? A line through a given point with the slope coinciding with the one of another line. Yes. (From your question, I understand that one may want to accomplish other options. What are they?)
            – blackened
            18 mins ago



















          2














          Use second line={(C)--($(C)+(D)-(E)$)}). The first one works as expected because (A)=(0,0)



          documentclass{article}
          usepackage{tikz}
          usetikzlibrary{intersections}
          usetikzlibrary{calc}
          begin{document}

          begin{tikzpicture}

          coordinate[label=A] (A) at (0,0);
          coordinate[label=B](B) at (2,4);
          coordinate[label=C] (C) at (8,0);
          coordinate[label=M] (M) at (4,0);

          path[name path=Circle] (B) circle [radius=3cm];
          path[name path=AB] (A)--(B);
          path[name path=BC] (B)--(C);
          path [name intersections={of=Circle and BC}];
          coordinate[label=E] (E) at (intersection-1);
          path [name intersections={of=Circle and AB}];
          coordinate[label=D] (D) at (intersection-1);

          draw[thick](A)--(B)--(C)--cycle;
          draw[thick](B) circle [radius=3cm];
          draw[thick](D)--(E) (M)--(B);

          % From a point draw a parallel line by calculating the vector
          coordinate[label=P] (P) at (intersection cs:first line={(B)--(C)}, second line={(A) -- +($(E)-(D)$)});

          % Here is my problem:
          coordinate[label=N] (N) at (intersection cs:first line={(B)--(M)}, second line={(C)--($(C)+(D)-(E)$)}); % <------


          draw[thick, red] (A)--(P) (C)--(N);

          end{tikzpicture}
          end{document}


          enter image description here






          share|improve this answer























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            2 Answers
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            active

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            2 Answers
            2






            active

            oldest

            votes









            active

            oldest

            votes






            active

            oldest

            votes









            2














            If you use the + syntax in this context, it seems not to always give you what one may expect. In general, + means "relative to the first coordinate of this path". But who knows what the first coordinate is in the context of intersection cs:? It is, however, not too difficult to produce the parallel lines just by computing the slope and using it. For the sake of clarity, I labeled all coordinates.



            documentclass{standalone}
            usepackage{tikz}
            usetikzlibrary{intersections}
            usetikzlibrary{calc}
            begin{document}

            begin{tikzpicture}

            coordinate[label=left:$A$] (A) at (0,0);
            coordinate[label=above:$B$] (B) at (2,4);
            coordinate[label=right:$C$] (C) at (8,0);
            coordinate[label=45:$M$] (M) at (4,0);

            draw[name path=Circle] (B) circle [radius=3cm];
            path[name path=AB] (A)--(B);
            path[name path=BC] (B)--(C);
            path [name intersections={of=Circle and BC}];
            coordinate[label=right:$E$] (E) at (intersection-1);
            path [name intersections={of=Circle and AB}];
            coordinate[label=left:$D$] (D) at (intersection-1);

            draw[thick](A)--(B)--(C)--cycle;
            %draw[thick](B) circle [radius=3cm];
            draw[thick](D)--(E) (M)--(B);

            % From a point draw a parallel line by calculating the vector
            path let p1=($(E)-(D)$),n1={atan2(y1,x1)} in
            ($(A)+(n1:1)$) coordinate (auxA)
            ($(C)+(n1:1)$) coordinate (auxC);
            coordinate[label=right:$P$] (P) at (intersection cs:first line={(B)--(C)},
            second line={(A) -- (auxA)});

            % Here is my problem:
            coordinate[label=below:$N$]
            (N) at (intersection cs:first line={(B)--(M)},
            second line={(C) -- (auxC)});

            draw[thick, red] (A)--(P) (C)--(N) ;

            end{tikzpicture}
            end{document}


            enter image description here



            As you see, the red lines are parallel.



            One may want cast this into a style:

            documentclass{standalone}
            usepackage{tikz}
            usetikzlibrary{intersections}
            usetikzlibrary{calc}
            begin{document}
            tikzset{line through/.style args={#1 parallel to line through #2 and #3 and
            length #4}{insert path={%
            let p1=($(#3)-(#2)$),n1={atan2(y1,x1)} in (#1) -- ++ (n1:#4)}}}
            begin{tikzpicture}

            coordinate[label=left:$A$] (A) at (0,0);
            coordinate[label=above:$B$] (B) at (2,4);
            coordinate[label=right:$C$] (C) at (8,0);
            coordinate[label=45:$M$] (M) at (4,0);

            draw[name path=Circle] (B) circle [radius=3cm];
            path[name path=AB] (A)--(B);
            path[name path=BC] (B)--(C);
            path [name intersections={of=Circle and BC}];
            coordinate[label=right:$E$] (E) at (intersection-1);
            path [name intersections={of=Circle and AB}];
            coordinate[label=left:$D$] (D) at (intersection-1);

            draw[thick](A)--(B)--(C)--cycle;
            %draw[thick](B) circle [radius=3cm];
            draw[thick](D)--(E) (M)--(B);

            % From a point draw a parallel line by calculating the vector
            path[line through=A parallel to line through E and D and length 1]
            coordinate (auxA)
            [line through=C parallel to line through E and D and length 1]
            coordinate (auxC);

            coordinate[label=right:$P$] (P) at (intersection cs:first line={(B)--(C)},
            second line={(A) -- (auxA)});

            % Here is my problem:
            coordinate[label=below:$N$]
            (N) at (intersection cs:first line={(B)--(M)},
            second line={(C) -- (auxC)});

            draw[thick, red] (A)--(P) (C)--(N) ;

            end{tikzpicture}
            end{document}





            share|improve this answer























            • Thank you. I was following this answer.
              – blackened
              27 mins ago












            • @blackened Yes, there it is very clear what the first point of the path is. Therefore, it is clear what + does. However, in the context of intersection cs: it is not clear to me where single paths start and end, and hence -- +(coordinate) may not be what one may thing it is. I am sorry if you feel that my wording is offensive, would like to apologize, and change it right away.
              – marmot
              25 mins ago












            • No worries at all. I just assumed that that answer encompassed all cases. How can I turn your approach to a tikz style definition?
              – blackened
              23 mins ago










            • @blackened What precisely do you want the style to accomplish? A line through a given point with the slope coinciding with the one of another line. (And rereading my original post I think my wording did indeed not reflect what I wanted to say.)
              – marmot
              20 mins ago










            • What precisely do you want the style to accomplish? A line through a given point with the slope coinciding with the one of another line. Yes. (From your question, I understand that one may want to accomplish other options. What are they?)
              – blackened
              18 mins ago
















            2














            If you use the + syntax in this context, it seems not to always give you what one may expect. In general, + means "relative to the first coordinate of this path". But who knows what the first coordinate is in the context of intersection cs:? It is, however, not too difficult to produce the parallel lines just by computing the slope and using it. For the sake of clarity, I labeled all coordinates.



            documentclass{standalone}
            usepackage{tikz}
            usetikzlibrary{intersections}
            usetikzlibrary{calc}
            begin{document}

            begin{tikzpicture}

            coordinate[label=left:$A$] (A) at (0,0);
            coordinate[label=above:$B$] (B) at (2,4);
            coordinate[label=right:$C$] (C) at (8,0);
            coordinate[label=45:$M$] (M) at (4,0);

            draw[name path=Circle] (B) circle [radius=3cm];
            path[name path=AB] (A)--(B);
            path[name path=BC] (B)--(C);
            path [name intersections={of=Circle and BC}];
            coordinate[label=right:$E$] (E) at (intersection-1);
            path [name intersections={of=Circle and AB}];
            coordinate[label=left:$D$] (D) at (intersection-1);

            draw[thick](A)--(B)--(C)--cycle;
            %draw[thick](B) circle [radius=3cm];
            draw[thick](D)--(E) (M)--(B);

            % From a point draw a parallel line by calculating the vector
            path let p1=($(E)-(D)$),n1={atan2(y1,x1)} in
            ($(A)+(n1:1)$) coordinate (auxA)
            ($(C)+(n1:1)$) coordinate (auxC);
            coordinate[label=right:$P$] (P) at (intersection cs:first line={(B)--(C)},
            second line={(A) -- (auxA)});

            % Here is my problem:
            coordinate[label=below:$N$]
            (N) at (intersection cs:first line={(B)--(M)},
            second line={(C) -- (auxC)});

            draw[thick, red] (A)--(P) (C)--(N) ;

            end{tikzpicture}
            end{document}


            enter image description here



            As you see, the red lines are parallel.



            One may want cast this into a style:

            documentclass{standalone}
            usepackage{tikz}
            usetikzlibrary{intersections}
            usetikzlibrary{calc}
            begin{document}
            tikzset{line through/.style args={#1 parallel to line through #2 and #3 and
            length #4}{insert path={%
            let p1=($(#3)-(#2)$),n1={atan2(y1,x1)} in (#1) -- ++ (n1:#4)}}}
            begin{tikzpicture}

            coordinate[label=left:$A$] (A) at (0,0);
            coordinate[label=above:$B$] (B) at (2,4);
            coordinate[label=right:$C$] (C) at (8,0);
            coordinate[label=45:$M$] (M) at (4,0);

            draw[name path=Circle] (B) circle [radius=3cm];
            path[name path=AB] (A)--(B);
            path[name path=BC] (B)--(C);
            path [name intersections={of=Circle and BC}];
            coordinate[label=right:$E$] (E) at (intersection-1);
            path [name intersections={of=Circle and AB}];
            coordinate[label=left:$D$] (D) at (intersection-1);

            draw[thick](A)--(B)--(C)--cycle;
            %draw[thick](B) circle [radius=3cm];
            draw[thick](D)--(E) (M)--(B);

            % From a point draw a parallel line by calculating the vector
            path[line through=A parallel to line through E and D and length 1]
            coordinate (auxA)
            [line through=C parallel to line through E and D and length 1]
            coordinate (auxC);

            coordinate[label=right:$P$] (P) at (intersection cs:first line={(B)--(C)},
            second line={(A) -- (auxA)});

            % Here is my problem:
            coordinate[label=below:$N$]
            (N) at (intersection cs:first line={(B)--(M)},
            second line={(C) -- (auxC)});

            draw[thick, red] (A)--(P) (C)--(N) ;

            end{tikzpicture}
            end{document}





            share|improve this answer























            • Thank you. I was following this answer.
              – blackened
              27 mins ago












            • @blackened Yes, there it is very clear what the first point of the path is. Therefore, it is clear what + does. However, in the context of intersection cs: it is not clear to me where single paths start and end, and hence -- +(coordinate) may not be what one may thing it is. I am sorry if you feel that my wording is offensive, would like to apologize, and change it right away.
              – marmot
              25 mins ago












            • No worries at all. I just assumed that that answer encompassed all cases. How can I turn your approach to a tikz style definition?
              – blackened
              23 mins ago










            • @blackened What precisely do you want the style to accomplish? A line through a given point with the slope coinciding with the one of another line. (And rereading my original post I think my wording did indeed not reflect what I wanted to say.)
              – marmot
              20 mins ago










            • What precisely do you want the style to accomplish? A line through a given point with the slope coinciding with the one of another line. Yes. (From your question, I understand that one may want to accomplish other options. What are they?)
              – blackened
              18 mins ago














            2












            2








            2






            If you use the + syntax in this context, it seems not to always give you what one may expect. In general, + means "relative to the first coordinate of this path". But who knows what the first coordinate is in the context of intersection cs:? It is, however, not too difficult to produce the parallel lines just by computing the slope and using it. For the sake of clarity, I labeled all coordinates.



            documentclass{standalone}
            usepackage{tikz}
            usetikzlibrary{intersections}
            usetikzlibrary{calc}
            begin{document}

            begin{tikzpicture}

            coordinate[label=left:$A$] (A) at (0,0);
            coordinate[label=above:$B$] (B) at (2,4);
            coordinate[label=right:$C$] (C) at (8,0);
            coordinate[label=45:$M$] (M) at (4,0);

            draw[name path=Circle] (B) circle [radius=3cm];
            path[name path=AB] (A)--(B);
            path[name path=BC] (B)--(C);
            path [name intersections={of=Circle and BC}];
            coordinate[label=right:$E$] (E) at (intersection-1);
            path [name intersections={of=Circle and AB}];
            coordinate[label=left:$D$] (D) at (intersection-1);

            draw[thick](A)--(B)--(C)--cycle;
            %draw[thick](B) circle [radius=3cm];
            draw[thick](D)--(E) (M)--(B);

            % From a point draw a parallel line by calculating the vector
            path let p1=($(E)-(D)$),n1={atan2(y1,x1)} in
            ($(A)+(n1:1)$) coordinate (auxA)
            ($(C)+(n1:1)$) coordinate (auxC);
            coordinate[label=right:$P$] (P) at (intersection cs:first line={(B)--(C)},
            second line={(A) -- (auxA)});

            % Here is my problem:
            coordinate[label=below:$N$]
            (N) at (intersection cs:first line={(B)--(M)},
            second line={(C) -- (auxC)});

            draw[thick, red] (A)--(P) (C)--(N) ;

            end{tikzpicture}
            end{document}


            enter image description here



            As you see, the red lines are parallel.



            One may want cast this into a style:

            documentclass{standalone}
            usepackage{tikz}
            usetikzlibrary{intersections}
            usetikzlibrary{calc}
            begin{document}
            tikzset{line through/.style args={#1 parallel to line through #2 and #3 and
            length #4}{insert path={%
            let p1=($(#3)-(#2)$),n1={atan2(y1,x1)} in (#1) -- ++ (n1:#4)}}}
            begin{tikzpicture}

            coordinate[label=left:$A$] (A) at (0,0);
            coordinate[label=above:$B$] (B) at (2,4);
            coordinate[label=right:$C$] (C) at (8,0);
            coordinate[label=45:$M$] (M) at (4,0);

            draw[name path=Circle] (B) circle [radius=3cm];
            path[name path=AB] (A)--(B);
            path[name path=BC] (B)--(C);
            path [name intersections={of=Circle and BC}];
            coordinate[label=right:$E$] (E) at (intersection-1);
            path [name intersections={of=Circle and AB}];
            coordinate[label=left:$D$] (D) at (intersection-1);

            draw[thick](A)--(B)--(C)--cycle;
            %draw[thick](B) circle [radius=3cm];
            draw[thick](D)--(E) (M)--(B);

            % From a point draw a parallel line by calculating the vector
            path[line through=A parallel to line through E and D and length 1]
            coordinate (auxA)
            [line through=C parallel to line through E and D and length 1]
            coordinate (auxC);

            coordinate[label=right:$P$] (P) at (intersection cs:first line={(B)--(C)},
            second line={(A) -- (auxA)});

            % Here is my problem:
            coordinate[label=below:$N$]
            (N) at (intersection cs:first line={(B)--(M)},
            second line={(C) -- (auxC)});

            draw[thick, red] (A)--(P) (C)--(N) ;

            end{tikzpicture}
            end{document}





            share|improve this answer














            If you use the + syntax in this context, it seems not to always give you what one may expect. In general, + means "relative to the first coordinate of this path". But who knows what the first coordinate is in the context of intersection cs:? It is, however, not too difficult to produce the parallel lines just by computing the slope and using it. For the sake of clarity, I labeled all coordinates.



            documentclass{standalone}
            usepackage{tikz}
            usetikzlibrary{intersections}
            usetikzlibrary{calc}
            begin{document}

            begin{tikzpicture}

            coordinate[label=left:$A$] (A) at (0,0);
            coordinate[label=above:$B$] (B) at (2,4);
            coordinate[label=right:$C$] (C) at (8,0);
            coordinate[label=45:$M$] (M) at (4,0);

            draw[name path=Circle] (B) circle [radius=3cm];
            path[name path=AB] (A)--(B);
            path[name path=BC] (B)--(C);
            path [name intersections={of=Circle and BC}];
            coordinate[label=right:$E$] (E) at (intersection-1);
            path [name intersections={of=Circle and AB}];
            coordinate[label=left:$D$] (D) at (intersection-1);

            draw[thick](A)--(B)--(C)--cycle;
            %draw[thick](B) circle [radius=3cm];
            draw[thick](D)--(E) (M)--(B);

            % From a point draw a parallel line by calculating the vector
            path let p1=($(E)-(D)$),n1={atan2(y1,x1)} in
            ($(A)+(n1:1)$) coordinate (auxA)
            ($(C)+(n1:1)$) coordinate (auxC);
            coordinate[label=right:$P$] (P) at (intersection cs:first line={(B)--(C)},
            second line={(A) -- (auxA)});

            % Here is my problem:
            coordinate[label=below:$N$]
            (N) at (intersection cs:first line={(B)--(M)},
            second line={(C) -- (auxC)});

            draw[thick, red] (A)--(P) (C)--(N) ;

            end{tikzpicture}
            end{document}


            enter image description here



            As you see, the red lines are parallel.



            One may want cast this into a style:

            documentclass{standalone}
            usepackage{tikz}
            usetikzlibrary{intersections}
            usetikzlibrary{calc}
            begin{document}
            tikzset{line through/.style args={#1 parallel to line through #2 and #3 and
            length #4}{insert path={%
            let p1=($(#3)-(#2)$),n1={atan2(y1,x1)} in (#1) -- ++ (n1:#4)}}}
            begin{tikzpicture}

            coordinate[label=left:$A$] (A) at (0,0);
            coordinate[label=above:$B$] (B) at (2,4);
            coordinate[label=right:$C$] (C) at (8,0);
            coordinate[label=45:$M$] (M) at (4,0);

            draw[name path=Circle] (B) circle [radius=3cm];
            path[name path=AB] (A)--(B);
            path[name path=BC] (B)--(C);
            path [name intersections={of=Circle and BC}];
            coordinate[label=right:$E$] (E) at (intersection-1);
            path [name intersections={of=Circle and AB}];
            coordinate[label=left:$D$] (D) at (intersection-1);

            draw[thick](A)--(B)--(C)--cycle;
            %draw[thick](B) circle [radius=3cm];
            draw[thick](D)--(E) (M)--(B);

            % From a point draw a parallel line by calculating the vector
            path[line through=A parallel to line through E and D and length 1]
            coordinate (auxA)
            [line through=C parallel to line through E and D and length 1]
            coordinate (auxC);

            coordinate[label=right:$P$] (P) at (intersection cs:first line={(B)--(C)},
            second line={(A) -- (auxA)});

            % Here is my problem:
            coordinate[label=below:$N$]
            (N) at (intersection cs:first line={(B)--(M)},
            second line={(C) -- (auxC)});

            draw[thick, red] (A)--(P) (C)--(N) ;

            end{tikzpicture}
            end{document}






            share|improve this answer














            share|improve this answer



            share|improve this answer








            edited 12 mins ago

























            answered 32 mins ago









            marmot

            85.6k497182




            85.6k497182












            • Thank you. I was following this answer.
              – blackened
              27 mins ago












            • @blackened Yes, there it is very clear what the first point of the path is. Therefore, it is clear what + does. However, in the context of intersection cs: it is not clear to me where single paths start and end, and hence -- +(coordinate) may not be what one may thing it is. I am sorry if you feel that my wording is offensive, would like to apologize, and change it right away.
              – marmot
              25 mins ago












            • No worries at all. I just assumed that that answer encompassed all cases. How can I turn your approach to a tikz style definition?
              – blackened
              23 mins ago










            • @blackened What precisely do you want the style to accomplish? A line through a given point with the slope coinciding with the one of another line. (And rereading my original post I think my wording did indeed not reflect what I wanted to say.)
              – marmot
              20 mins ago










            • What precisely do you want the style to accomplish? A line through a given point with the slope coinciding with the one of another line. Yes. (From your question, I understand that one may want to accomplish other options. What are they?)
              – blackened
              18 mins ago


















            • Thank you. I was following this answer.
              – blackened
              27 mins ago












            • @blackened Yes, there it is very clear what the first point of the path is. Therefore, it is clear what + does. However, in the context of intersection cs: it is not clear to me where single paths start and end, and hence -- +(coordinate) may not be what one may thing it is. I am sorry if you feel that my wording is offensive, would like to apologize, and change it right away.
              – marmot
              25 mins ago












            • No worries at all. I just assumed that that answer encompassed all cases. How can I turn your approach to a tikz style definition?
              – blackened
              23 mins ago










            • @blackened What precisely do you want the style to accomplish? A line through a given point with the slope coinciding with the one of another line. (And rereading my original post I think my wording did indeed not reflect what I wanted to say.)
              – marmot
              20 mins ago










            • What precisely do you want the style to accomplish? A line through a given point with the slope coinciding with the one of another line. Yes. (From your question, I understand that one may want to accomplish other options. What are they?)
              – blackened
              18 mins ago
















            Thank you. I was following this answer.
            – blackened
            27 mins ago






            Thank you. I was following this answer.
            – blackened
            27 mins ago














            @blackened Yes, there it is very clear what the first point of the path is. Therefore, it is clear what + does. However, in the context of intersection cs: it is not clear to me where single paths start and end, and hence -- +(coordinate) may not be what one may thing it is. I am sorry if you feel that my wording is offensive, would like to apologize, and change it right away.
            – marmot
            25 mins ago






            @blackened Yes, there it is very clear what the first point of the path is. Therefore, it is clear what + does. However, in the context of intersection cs: it is not clear to me where single paths start and end, and hence -- +(coordinate) may not be what one may thing it is. I am sorry if you feel that my wording is offensive, would like to apologize, and change it right away.
            – marmot
            25 mins ago














            No worries at all. I just assumed that that answer encompassed all cases. How can I turn your approach to a tikz style definition?
            – blackened
            23 mins ago




            No worries at all. I just assumed that that answer encompassed all cases. How can I turn your approach to a tikz style definition?
            – blackened
            23 mins ago












            @blackened What precisely do you want the style to accomplish? A line through a given point with the slope coinciding with the one of another line. (And rereading my original post I think my wording did indeed not reflect what I wanted to say.)
            – marmot
            20 mins ago




            @blackened What precisely do you want the style to accomplish? A line through a given point with the slope coinciding with the one of another line. (And rereading my original post I think my wording did indeed not reflect what I wanted to say.)
            – marmot
            20 mins ago












            What precisely do you want the style to accomplish? A line through a given point with the slope coinciding with the one of another line. Yes. (From your question, I understand that one may want to accomplish other options. What are they?)
            – blackened
            18 mins ago




            What precisely do you want the style to accomplish? A line through a given point with the slope coinciding with the one of another line. Yes. (From your question, I understand that one may want to accomplish other options. What are they?)
            – blackened
            18 mins ago











            2














            Use second line={(C)--($(C)+(D)-(E)$)}). The first one works as expected because (A)=(0,0)



            documentclass{article}
            usepackage{tikz}
            usetikzlibrary{intersections}
            usetikzlibrary{calc}
            begin{document}

            begin{tikzpicture}

            coordinate[label=A] (A) at (0,0);
            coordinate[label=B](B) at (2,4);
            coordinate[label=C] (C) at (8,0);
            coordinate[label=M] (M) at (4,0);

            path[name path=Circle] (B) circle [radius=3cm];
            path[name path=AB] (A)--(B);
            path[name path=BC] (B)--(C);
            path [name intersections={of=Circle and BC}];
            coordinate[label=E] (E) at (intersection-1);
            path [name intersections={of=Circle and AB}];
            coordinate[label=D] (D) at (intersection-1);

            draw[thick](A)--(B)--(C)--cycle;
            draw[thick](B) circle [radius=3cm];
            draw[thick](D)--(E) (M)--(B);

            % From a point draw a parallel line by calculating the vector
            coordinate[label=P] (P) at (intersection cs:first line={(B)--(C)}, second line={(A) -- +($(E)-(D)$)});

            % Here is my problem:
            coordinate[label=N] (N) at (intersection cs:first line={(B)--(M)}, second line={(C)--($(C)+(D)-(E)$)}); % <------


            draw[thick, red] (A)--(P) (C)--(N);

            end{tikzpicture}
            end{document}


            enter image description here






            share|improve this answer




























              2














              Use second line={(C)--($(C)+(D)-(E)$)}). The first one works as expected because (A)=(0,0)



              documentclass{article}
              usepackage{tikz}
              usetikzlibrary{intersections}
              usetikzlibrary{calc}
              begin{document}

              begin{tikzpicture}

              coordinate[label=A] (A) at (0,0);
              coordinate[label=B](B) at (2,4);
              coordinate[label=C] (C) at (8,0);
              coordinate[label=M] (M) at (4,0);

              path[name path=Circle] (B) circle [radius=3cm];
              path[name path=AB] (A)--(B);
              path[name path=BC] (B)--(C);
              path [name intersections={of=Circle and BC}];
              coordinate[label=E] (E) at (intersection-1);
              path [name intersections={of=Circle and AB}];
              coordinate[label=D] (D) at (intersection-1);

              draw[thick](A)--(B)--(C)--cycle;
              draw[thick](B) circle [radius=3cm];
              draw[thick](D)--(E) (M)--(B);

              % From a point draw a parallel line by calculating the vector
              coordinate[label=P] (P) at (intersection cs:first line={(B)--(C)}, second line={(A) -- +($(E)-(D)$)});

              % Here is my problem:
              coordinate[label=N] (N) at (intersection cs:first line={(B)--(M)}, second line={(C)--($(C)+(D)-(E)$)}); % <------


              draw[thick, red] (A)--(P) (C)--(N);

              end{tikzpicture}
              end{document}


              enter image description here






              share|improve this answer


























                2












                2








                2






                Use second line={(C)--($(C)+(D)-(E)$)}). The first one works as expected because (A)=(0,0)



                documentclass{article}
                usepackage{tikz}
                usetikzlibrary{intersections}
                usetikzlibrary{calc}
                begin{document}

                begin{tikzpicture}

                coordinate[label=A] (A) at (0,0);
                coordinate[label=B](B) at (2,4);
                coordinate[label=C] (C) at (8,0);
                coordinate[label=M] (M) at (4,0);

                path[name path=Circle] (B) circle [radius=3cm];
                path[name path=AB] (A)--(B);
                path[name path=BC] (B)--(C);
                path [name intersections={of=Circle and BC}];
                coordinate[label=E] (E) at (intersection-1);
                path [name intersections={of=Circle and AB}];
                coordinate[label=D] (D) at (intersection-1);

                draw[thick](A)--(B)--(C)--cycle;
                draw[thick](B) circle [radius=3cm];
                draw[thick](D)--(E) (M)--(B);

                % From a point draw a parallel line by calculating the vector
                coordinate[label=P] (P) at (intersection cs:first line={(B)--(C)}, second line={(A) -- +($(E)-(D)$)});

                % Here is my problem:
                coordinate[label=N] (N) at (intersection cs:first line={(B)--(M)}, second line={(C)--($(C)+(D)-(E)$)}); % <------


                draw[thick, red] (A)--(P) (C)--(N);

                end{tikzpicture}
                end{document}


                enter image description here






                share|improve this answer














                Use second line={(C)--($(C)+(D)-(E)$)}). The first one works as expected because (A)=(0,0)



                documentclass{article}
                usepackage{tikz}
                usetikzlibrary{intersections}
                usetikzlibrary{calc}
                begin{document}

                begin{tikzpicture}

                coordinate[label=A] (A) at (0,0);
                coordinate[label=B](B) at (2,4);
                coordinate[label=C] (C) at (8,0);
                coordinate[label=M] (M) at (4,0);

                path[name path=Circle] (B) circle [radius=3cm];
                path[name path=AB] (A)--(B);
                path[name path=BC] (B)--(C);
                path [name intersections={of=Circle and BC}];
                coordinate[label=E] (E) at (intersection-1);
                path [name intersections={of=Circle and AB}];
                coordinate[label=D] (D) at (intersection-1);

                draw[thick](A)--(B)--(C)--cycle;
                draw[thick](B) circle [radius=3cm];
                draw[thick](D)--(E) (M)--(B);

                % From a point draw a parallel line by calculating the vector
                coordinate[label=P] (P) at (intersection cs:first line={(B)--(C)}, second line={(A) -- +($(E)-(D)$)});

                % Here is my problem:
                coordinate[label=N] (N) at (intersection cs:first line={(B)--(M)}, second line={(C)--($(C)+(D)-(E)$)}); % <------


                draw[thick, red] (A)--(P) (C)--(N);

                end{tikzpicture}
                end{document}


                enter image description here







                share|improve this answer














                share|improve this answer



                share|improve this answer








                edited 7 mins ago

























                answered 24 mins ago









                Hafid Boukhoulda

                1,3621515




                1,3621515






























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