Wie zeichne ich den Inkreis eines Dreiecks in TikZ?

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\documentclass[border=5pt, varwidth]{standalone}
%\documentclass[]{article}
\usepackage[utf8]{inputenc}
\usepackage[ngerman]{babel} 
\usepackage[T1]{fontenc}
\usepackage{amsmath,amsfonts,amssymb}
\usepackage{tikz}
%   \usetikzlibrary{calc}
\begin{document}
\begin{tikzpicture}[scale=1]
% Koordinaten der Eckpunkte
\def\xA{0}
\def\yA{0}
\def\xB{5}
\def\yB{0}
\def\xC{3}
\def\yC{2}
\coordinate (A) at (\xA,\yA);
\coordinate (B) at (\xB,\yB);
\coordinate (C) at (\xC,\yC);
% Seitenlängen
\pgfmathsetmacro{\a}{sqrt((\xA - \xC)^2 + (\yA - \yC)^2)}
\pgfmathsetmacro{\b}{sqrt((\xB - \xC)^2 + (\yB - \yC)^2)}
\pgfmathsetmacro{\c}{sqrt((\xA - \xB)^2 + (\yA - \yB)^2)}
% Inkreis
% Koordinate des Inkreismittelpunktes
\pgfmathsetmacro{\P}{\a+\b+\c}
\pgfmathsetmacro{\xW}{(\a*\xA + \b*\xB + \c*\xC)/\P}
\pgfmathsetmacro{\yW}{(\a*\yA + \b*\yB + \c*\yC)/\P}
\coordinate (W) at (\xW,\yW);
% Inkreisradius
\pgfmathsetmacro{\s}{\P/2}
\pgfmathsetmacro{\r}{sqrt(((\s-\a)*(\s-\b)*(\s-\c))/\s)}
% Inkreis zeichnen
 
 
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