Tangential, cyclic & bicentric quadrilaterals

Construct tangential, cyclic and bicentric quadrilaterals.

Cyclic quadrilateral:

Tangential quadrilateral:

Bicentric quadrilaterals using intersections:

Bicentric quadrilateral:

Animating the starting point:

Right kite as a bicentric:

Edit and compile if you like:

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% Author: Izaak Neutelings (January 2022)
\documentclass[border=3pt,tikz]{standalone}
\usetikzlibrary{calc}
\usetikzlibrary{intersections}
\usepackage[outline]{contour} % glow around text
\contourlength{0.9pt}
\colorlet{myred}{red!80!black}
\colorlet{myblue}{blue!80!black}
\colorlet{mygreen}{green!80!black}
\colorlet{myorange}{orange!90!black}
\colorlet{mydarkred}{red!60!black}
\colorlet{mydarkblue}{blue!50!black}
\colorlet{mydarkgreen}{green!50!black}
\colorlet{mydarkorange}{orange!70!black}
\newcommand\rightAngle[4]{
  \pgfmathanglebetweenpoints{\pgfpointanchor{#2}{center}}{\pgfpointanchor{#1}{center}}
  \coordinate (tmpRA) at ($(#2)+(\pgfmathresult+45:#4)$);
  \draw[mydarkblue] ($(#2)!(tmpRA)!(#1)$) -- (tmpRA) -- ($(#2)!(tmpRA)!(#3)$);
}
\tikzset{
  angshift/.initial=1,   % shift from origin/center
  angcol/.style={draw=#1!80!black,fill=#1!30}, % shorthand to fill (light) & draw (dark)
  angcol/.default={myblue},
  pics/right angle/.style args={(#1)-(#2)-(#3):#4}{ % right angle
    code={
      \tikzset{angshift/.get=\angshift}
      \pgfmathanglebetweenpoints{\pgfpointanchor{#2}{center}}{\pgfpointanchor{#1}{center}}
      \pgfmathsetmacro\tmpAngA{\pgfmathresult}
      \coordinate (tmpS) at (\tmpAngA+45:\angshift*0.01); % shift
      \coordinate (tmp#1) at ($(#1)+(tmpS)$);
      \coordinate (tmp#2) at ($(#2)+(tmpS)$);
      \coordinate (tmp#3) at ($(#3)+(tmpS)$);
      \coordinate (tmpRA) at ($(tmp#2)+(\tmpAngA+45:#4)$);
      \fill[pic actions,draw=none] % fill square area
        ($(tmp#2)!(tmpRA)!(tmp#1)$) -- (tmpRA) -- ($(tmp#2)!(tmpRA)!(tmp#3)$) -- (tmp#2) -- cycle;
      \draw[pic actions,fill=none] % draw orthogonal mark
        ($(tmp#2)!(tmpRA)!(tmp#1)$) -- (tmpRA) -- ($(tmp#2)!(tmpRA)!(tmp#3)$);
    }
  }
}
 
 
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Click to download: quadrilaterals_bicentric.tex • quadrilaterals_bicentric.pdf
Open in Overleaf: quadrilaterals_bicentric.tex