How to repair Dimension too large when I draw this triangle?

Question

I use this code to draw triangle. When I choose a = b = c = 5, I got the result.

\documentclass[12pt, border = 1mm]{standalone}
\usepackage{tikz}
\usepackage{tikz-3dplot}
\usetikzlibrary{intersections,calc,backgrounds}
\begin{document}
    \tdplotsetmaincoords{70}{80}
    \begin{tikzpicture}[tdplot_main_coords,line join = round, line cap = round]

    \pgfmathsetmacro{\a}{5} 
    \pgfmathsetmacro{\b}{5} 
    \pgfmathsetmacro{\c}{5} 
    \pgfmathsetmacro\myr{{sqrt(- pow(\a,2) *pow(\b,2)* pow(\c,2)/(pow(\a,4)  + pow(\b,4)  + pow(\c,4)- 2 *pow(\a,2) *pow(\b,2)  - 2*pow(\c,2) *pow(\b,2)-2*pow(\c,2) *pow(\a,2) ))}}
    \coordinate (A) at (0,0,0);
    \coordinate (B) at (\c,0,0);
    \coordinate (C) at  ({(pow(\b,2) + pow(\c,2) - pow(\a,2))/(2*\c)},{sqrt((\a+\b-\c) *(\a-\b+\c) *(-\a+\b+\c)* (\a+\b+\c))/(2*\c)},0);
    \coordinate (T) at  (\c/2, {\c* (\a*\a + \b*\b - \c*\c)/(2*sqrt((\a+\b-\c) *(\a-\b+\c)* (-\a+\b+\c)* (\a+\b+\c)))},0);

    \foreach \point/\position in {A/left,B/below,C/above,T/below}
    {
        \fill (\point) circle (1.8pt);
        \node[\position=3pt] at (\point) {$\point$};
    }
    \begin{scope}[canvas is xy plane at z=0]
    \draw[thick] (T) circle (\myr); 
    \end{scope} 
    \end{tikzpicture}
    \end{document}

If I use a = b = c = 6 or larger, I cannot obtain the result. How can I get the result?

Answer 1

There are some standard ways to deal with this. One of them is to use the fpu library. (fpu is mentioned in the comment by John Kormylo, but I do not have the problems mentioned there.) However, as you noted yourself in some constructions like arc just switching on fpu can lead to problems. In order to make things more convenient for you, I added a macro \PgfmathsetmacroFPU, which switches the library on locally, parses the expression, and "smuggles" the result out of the group. Therefore, the definition of the macro will be local, just like in the case of the ordinary \pgfmathsetmacro. Note that \pgfmathsmuggle has been added to the more recent versions of pgf, so if you have an outdated TeX installation it may not work. Sorry overleaf users! Further information on smuggling as well as alternative commands can be found in the answers to this question.

\documentclass[12pt, border = 1mm]{standalone}
\usepackage{tikz}
\usepackage{tikz-3dplot}
\usetikzlibrary{intersections,calc,backgrounds,fpu} 
\newcommand{\PgfmathsetmacroFPU}[2]{\begingroup%
\pgfkeys{/pgf/fpu,/pgf/fpu/output format=fixed}%
\pgfmathsetmacro{#1}{#2}%
\pgfmathsmuggle#1\endgroup}
\begin{document}
\tdplotsetmaincoords{70}{80}
\begin{tikzpicture}[tdplot_main_coords,line join = round, line cap = round]
    \pgfmathsetmacro{\a}{6} 
    \pgfmathsetmacro{\b}{6} 
    \pgfmathsetmacro{\c}{6} 
    \PgfmathsetmacroFPU{\myr}{{sqrt(-
     pow(\a,2) *pow(\b,2)* pow(\c,2)/ (pow(\a,4)  + pow(\b,4)  + pow(\c,4)- 2
     *pow(\a,2) *pow(\b,2)  - 2*pow(\c,2) *pow(\b,2)-2*pow(\c,2) *pow(\a,2) ))}}
    \PgfmathsetmacroFPU{\Angleone}{-90} 
    \PgfmathsetmacroFPU{\Angletwo}{60}
    \coordinate (E) at ({\c/2 + \myr*cos(\Angleone)},{\c* (\a*\a + \b*\b -
     \c*\c)/(2*sqrt((\a+\b-\c) *(\a-\b+\c)* (-\a+\b+\c)* (\a+\b+\c))) +
     \myr*sin(\Angleone)},0 );  \coordinate (F) at ({\c/2 +
    \myr*cos(\Angletwo)},{\c* (\a*\a + \b*\b - \c*\c)/(2*sqrt((\a+\b-\c)
     *(\a-\b+\c)* (-\a+\b+\c)* (\a+\b+\c))) + \myr*sin(\Angletwo)},0 ); 
    \coordinate (A) at (0,0,0);
    \coordinate (B) at (\c,0,0);
    \coordinate (C) at  ({(pow(\b,2) + pow(\c,2) - pow(\a,2))/(2*\c)},{sqrt((\a+\b-\c) *(\a-\b+\c) *(-\a+\b+\c)* (\a+\b+\c))/(2*\c)},0);
    \coordinate (T) at  (\c/2, {\c* (\a*\a + \b*\b - \c*\c)/(2*sqrt((\a+\b-\c) *(\a-\b+\c)* (-\a+\b+\c)* (\a+\b+\c)))},0);
    \foreach \point/\position in {A/left,B/below,C/above,T/below}
    {
        \fill (\point) circle (1.8pt);
        \node[\position=3pt] at (\point) {$\point$};
    }
    \begin{scope}[canvas is xy plane at z=0]
    \draw[thick] (T) circle (\myr); 
    \end{scope}
    \pgfmathsetmacro{\Angleone}{-90} 
    \pgfmathsetmacro{\Angletwo}{60}  
    \draw[thick] (E) arc[start angle=\Angleone,end angle=\Angletwo,radius=\myr]; 
\end{tikzpicture}
\end{document}