Wie zeichne ich den Inkreis eines Dreiecks in TikZ?

\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
\draw[blue] (W) circle[radius=\r];

% Winkelhalbierende
\draw (W) -- (A);
\draw (W) -- (B);
\draw (W) -- (C);

\draw[] (A) -- (B) -- (C) -- cycle;
\end{tikzpicture}

\end{document}