PWWs-01-10

Trisection of a Line Segment

PWWs-01-10
\documentclass[tikz, border=2pt]{standalone}
\usetikzlibrary{calc}
\usetikzlibrary{math}
\begin{document}
\begin{tikzpicture}[line width=1pt]
  \tikzmath{
    \r = 2;
  }
  \def\template#1; {
    \draw #1 circle [radius=\r];
    \draw #1 ++(\r, 0) circle [radius=\r];
    \draw #1 -- ++(\r, 0);
  }

  \coordinate (O) at (0, 0);
  \template{(O)};
  \node[left] (A) at (O) {$A$};
  \node[right] (B) at ($(O) + (\r, 0)$) {$B$};

  \coordinate (O1) at (3.5*\r, 0);
  \template{(O1)};
  \coordinate (C1) at ($(O1) + (60:\r)$);
  \node[above] () at (C1) {$C$};
  \coordinate (D1) at ($(O1) + (-120:\r)$);
  \node[below] () at (D1) {$D$};
  \draw (C1) -- (D1);

  \coordinate (O2) at (0, -3*\r);
  \template{(O2)};
  \coordinate (B2) at ($(O2) + (\r, 0)$);
  \coordinate (C2) at ($(O2) + (60:\r)$);
  \coordinate (D2) at ($(O2) + (-120:\r)$);
  \coordinate (E2) at ($(O2) + (-60:0.5*\r)$);
  \coordinate (G2) at ($(O2) + (-60:\r)$);
  \draw (C2) -- (D2);
  \draw (D2) -- (B2);
  \draw (O2) -- (G2);
  \node[right=2mm] () at (E2) {$E$};

  \coordinate (O3) at (3.5*\r, -3*\r);
  \template{(O3)};
  \coordinate (B3) at ($(O3) + (\r, 0)$);
  \coordinate (C3) at ($(O3) + (60:\r)$);
  \coordinate (D3) at ($(O3) + (-120:\r)$);
  \coordinate (E3) at ($(O3) + (-60:0.5*\r)$);
  \coordinate (G3) at ($(O3) + (-60:\r)$);
  \draw (C3) -- (D3);
  \draw (D3) -- (B3);
  \draw (O3) -- (G3);
  \draw (E3) -- (C3);
  \draw[dashed] (B3) -- (C3);
  \node[left] () at (O3) {$A$};
  \node[right] () at (B3) {$B$};
  \node[above] () at (C3) {$C$};
  \node[below] () at (D3) {$D$};
  \node[right=2mm] () at (E3) {$E$};
  \node[below right] (F3) at ($(O3) + (0.34*\r, 0)$) {$F$};

  \node[below=2cm, align=center] () at ($(O2) + (2.25*\r, 0)$) {
      $\displaystyle\overline{AF} = \frac{1}{3}\cdot\overline{AB}$
    }
\end{tikzpicture}
\end{document}

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