等边三角形的内接圆

Question

我正在尝试画等边三角形。我做错了什么。

\documentclass{article}
\usepackage{tkz-euclide}

\begin{document}
    \begin{tikzpicture}[scale=1]
        \tkzDefPoint(0,0){A}
        \tkzDefPoint(4,0){B}
        \tkzDefTriangle[equilateral](A,B)
        \tkzGetPoint{C}
        \tkzDefCircle[in](A,B,C)
        \tkzGetPoint{O} \tkzGetLength{rIN}
        \tkzDrawPoints(A,B,C,O)
        \tkzDrawCircle[R,blue](O,\rIN pt)
        \tkzLabelPoints(A,B,C,O)
        \tkzDrawPolygon(A,B,C)
    \end{tikzpicture}
\end{document}

Answer 1

我怀疑在将圆内接于等边三角形时存在某种错误。它与许多其他三角形配合得很好，但当你接近 60° 时，它就无法做到这一点。例如，角度为 59.9°：

\documentclass{article}
\usepackage{tkz-euclide}

\begin{document}
    \begin{tikzpicture}[scale=1]
       
        \coordinate (A) at (0,0);
        \coordinate (B) at (4,0);
        \coordinate (C) at (59.9:4);

        \tkzDefCircle[in](A,B,C)
        
        \tkzGetPoint{O} \tkzGetLength{rIN}
        \tkzDrawPoints(A,B,C,O)
        \tkzDrawCircle[R,blue](O,\rIN pt)
        \tkzLabelPoints(A,B,C,O)
        \tkzDrawPolygon(A,B,C)
              
    \end{tikzpicture}
    
\end{document}

但当角度达到 59.99° 时，它就失败了：

所以你没有做错什么。如果你想用 来绘制它tkz-euclide，你可以“手工”绘制：

\documentclass{article}
\usepackage{tkz-euclide}

\begin{document}
    \begin{tikzpicture}[scale=1]
       
        \coordinate (A) at (0,0);
        \coordinate (B) at (4,0);
        \coordinate (C) at (60:4);

        \tkzDefBarycentricPoint(A=1,B=1,C=1) \tkzGetPoint{O}
        \tkzInterLL(A,O)(C,B) \tkzGetPoint{A'}
        \tkzDrawCircle[color=blue](O,A')
        
        
       \tkzDrawPoints(A,B,C,O)
        \tkzLabelPoints(A,B,C,O)
        \tkzDrawPolygon(A,B,C)
              
    \end{tikzpicture}
\end{document}

Answer 2

采用简单的 TikZ 方式。

\documentclass[tikz,border=5mm]{standalone}
\begin{document}
\begin{tikzpicture}
\def\R{2} % radius of circumcircle
\pgfmathsetmacro{\r}{\R/2} % radius of incircle
\path
(90:\R) coordinate (A) node[above]{$A$}
(210:\R) coordinate (B) node[below left]{$B$}
(-30:\R) coordinate (C) node[below right]{$C$};
\fill[red] (0,0) circle(1.5pt);
\draw[red] (0,0) circle(\r);
\draw (A)--(B)--(C)--cycle;
\end{tikzpicture}
\end{document}

Answer 3

用方法解决tangent问题。

\documentclass[margin=3mm]{standalone}

\usepackage{tkz-euclide}

\begin{document}

\begin{tikzpicture}[rotate=180]
    \tkzDefPoint(0, 0){CircleCenter}
    \tkzDrawCircle[R,very thick](CircleCenter,3cm)

    % Define 3 points on circle. Angles for equilateral triangle
    
    \tkzDefPoint( 90:3){C}
    \tkzDefPoint(210:3){A}
    \tkzDefPoint(330:3){B}
    

    % Tangents
    \tkzDefLine[perpendicular=through C](CircleCenter,C)\tkzGetPoint{C2}
    \tkzDefLine[perpendicular=through A](CircleCenter,A)\tkzGetPoint{A2}
    \tkzDefLine[perpendicular=through B](CircleCenter,B)\tkzGetPoint{B2}
   

    % Find the points by intersecting the tangents
    \tkzInterLL(C,C2)(A,A2)\tkzGetPoint{CC}
    \tkzInterLL(A,A2)(B,B2)\tkzGetPoint{AA}
    \tkzInterLL(B,B2)(C,C2)\tkzGetPoint{BB}
    
    % Draw triangle
    \tkzDrawPolygon[very thick](AA,BB,CC)

    % Draw points
    \tkzDrawPoints[size=3pt](CircleCenter)
    \tkzDrawPoints[size=3pt](AA,BB,CC)
    \node at (CircleCenter)[below right]{O};
    \node at (BB)[left]{B};
    \node at (CC)[right]{C};
    \node at (AA)[above]{A};
 
\end{tikzpicture}

\结束{文档}