Understanding the code and trying to learn

Question

I have used the following code to create triangles inside a circle which works really well. Can anybody point me in the direction to somewhere I can learn to adapt this code so for example creating the double angle rule or cyclic quadrilaterals?

\documentclass[tikz,margin=2mm,5pt]{standalone}
\usetikzlibrary {angles,quotes}
\usetikzlibrary{calc,positioning}
\pgfmathsetseed{\pdfuniformdeviate 10000000}

\usepackage{scrextend}
\changefontsizes[10pt]{5pt}

\pgfdeclarelayer{back}
    \pgfdeclarelayer{front}
    \pgfsetlayers{back,main,front}


\begin{document}
\foreach \p in {{A/2,B/2,C/4,D/5},{A/2,B/3,C/4,D/6,E/9}}{
  \begin{tikzpicture}
    \pgfmathsetmacro\r{2cm} \pgfmathsetmacro\ld{3mm}
    \foreach \l/\v[evaluate=\v as \s using \s + \v,remember=\s as \s (initially 0),
    remember=\l as \ls,remember=\v as \lv] in \p{}
    \pgfmathsetmacro\unit{360/\s} \pgfmathsetmacro\ai{rnd*360}
    \fill circle(1pt) coordinate (I); \draw circle(\r pt);
    \draw (\ai:\r pt)
    \foreach \l/\v[evaluate=\v as \s using \psum + \v, remember=\s as \psum (initially 0)]
    in \p {-- ({\unit*\psum+\ai}:\r pt) coordinate (\l)} -- cycle;
    \foreach \l/\v in \p {
      \draw (I) -- (\l); \fill (\l) circle (1pt);
      \node at ($(I)!\r pt+\ld pt!(\l)$) {$\l$};
      }
    \node[circle,inner sep=0.1pt] at ($(I) + (\ai:3mm)$) {$O$}; %labeled O But     Referenced I
    \foreach \l/\v[remember=\l as \pl (initially \ls),remember=\v as \pv (initially \lv)]
    in \p {\node at ($(I)!\r pt+\ld pt!($(\pl)!.5!(\l)$)$) {\pv};}
     \end{tikzpicture}
    }
 \end{document}

I don't know if this out of the purview of this site, I am asking for help on where to learn (but obviously any help would be nice). Thanks

Answer 1

Your code:

• contain error(s), therefore we cannot test it;
• is very -- to my opinion unnecessary -- complex and unclear (I must confes, that I went lost in it);
• is not entirely clear, what should your code produce.
• If your code should draw circle around (any) triangle, then this can be done on far more simple way to do this:
  • first draw circle,
  • then on circle define three (random) points for triangle corners coordinates
  • draw lines between defined coordinates.

\documentclass[border=3.141592=12mm]{standalone}
\usepackage{tikz}
\usetikzlibrary{arrows.meta,
                positioning,
                quotes}
\pgfmathsetseed{\pdfuniformdeviate 10000000} 

\begin{document}
    \begin{tikzpicture}[
trig format=rad,
dot/.style = {circle, fill, inner sep=1pt, outer sep=0pt},
ang/.style = {draw=red, <->,
              angle radius = 3mm,
              angle eccentricity=1.2,
              }
                        ]
\pgfmathsetmacro{\r}{2}
\pgfmathsetmacro{\R}{\r+0.3}
% circle
\draw (0,0) coordinate (O) circle[radius=\r];
% triangles' corners coordinates and labels
\foreach \c/\l in {rand/A, rand/B, rand/C}  % define random coefficients 
                                            % for calculations of triangle's 
                                            % corners coordinates on circle
                                            % and define corners names
{
\pgfmathsetmacro{\C}{2*pi*\c}               % calculate triangle coordinates
  \node (\l) [dot] at (\C:\r) {};           % draw dots at triangle corners
  \draw[-Stealth, gray, very thin]          % draw arrows from circle center 
                                            % to triangle's corners, 
                                            % if not needed, just delete this line 
        (0,0)   -- (\l);
  \path (\l) -- (\C:\R) node {\l};          % define corners labels coordinates,
                                            % they are in direction of vector 
                                            % from circle origin to dot node
}
% triangle
\draw[cyan]   
        (A) -- (B) -- (C) -- (A);           % draw trangle
    \end{tikzpicture}
\end{document}

An random result is (it is different after each compilation, is this what you after?):

Answer 2

Another pedagogical (I hope) example:

\documentclass[border=10pt]{standalone}
\usepackage{tikz}

\begin{document}
    \begin{tikzpicture}[scale=1.5]
    % rotate (six time) a square around hi center
         \foreach \i in {15,30,...,90}
         \filldraw[blue!60!brown,line width=1pt,rotate around={\i:(4,0)}]
         (0,0)--(4,4)--(8,0)--(4,-4)--(0,0);
         % fix a circular zone where to place the Euler picture
         \begin{scope}
         \path [clip] (4,0) circle (2.9);
         \node at (4,0) () {\includegraphics[width=10cm]{Euler.png}};
         \end{scope}
         %the circle atound the picture
         \draw[white,line width=4pt] (4,0) circle(2.9);
         %some text on top snd on bottom of the picture
         \node[white] at (4,3.15) () {\LARGE \bfseries L. Euler};
         \node[white] at (4,-3.2) () {\huge \bfseries $e^{i\pi}+1=0$};
    \end{tikzpicture}
\end{document}

The output:

Answer 3

Two more examples:

\documentclass[10pt,a4paper]{article}
\usepackage{tikz}
\usetikzlibrary{calc,snakes}
\usetikzlibrary{ decorations.markings}

\begin{document}
    \begin{tikzpicture}[scale=.6]   
        %muretto
        \filldraw[gray!60] (0.25,.25)--(0,0)--(11.75,0)--(12,.25);
        \filldraw[gray] (0,0) rectangle (11.75,-.5);
        \filldraw[gray!40] (11.75,0)--(11.75,-.5)--(12,-.25)--(12,.25);
        % lance
        \foreach \i in {1,1.5,...,6}
            \draw[line width=3pt,-latex] (\i,0.1)--(\i,\i-.1);
        \foreach \i in {.5,1,...,5}
        \draw[line width=3pt,-latex] (\i+6,0.1)--(\i+6,5.9-\i);
    \end{tikzpicture}
    
    \vspace{3cm}
    
    \begin{tikzpicture}[scale=1.1]
         \filldraw[snake=snake,blue,line width=1pt]
         (0,0)--(4,4)--(8,0)--(4,-4)--(0,0);
         \filldraw[blue] (4,0) circle(3.25);
         \shade[ball color=gray!5] (4,0) circle (2);
         \foreach \i in {2,2.417,2.824,3.25}
         \draw[yellow!30,line width=2.5pt] (4,0) circle(\i);
         \node[blue] at (4,0) () {\Huge \bfseries $e^{i\pi}+1=0$};
         \filldraw[white] (4,3.5) circle(2pt);
    \end{tikzpicture}
\end{document}

Output: