\documentclass[varwidth=true, border=2pt]{standalone}
\usepackage{tikz}
\usetikzlibrary{arrows,positioning, calc, shapes.misc}
\tikzset{
    %Define standard arrow tip
    >=stealth',
    % Define arrow style
    pil/.style={->,thick}
}

\tikzstyle{point}=[    thick,
    draw=gray,
    cross out,
    inner sep=0pt,
    minimum width=4pt,
    minimum height=4pt]

\begin{document}
  \begin{tikzpicture}
    % draw the background
    % -2/cos(30°) = 4/sqrt(3) \approx 2.309 - Umkreisradius
    %  2*tan(30°) = 2/sqrt(3) \approx 1.155 - Inkreisradius

    \node[point] (TriangleCenter) at (0,0) {};
    \draw[thick, draw=blue] (TriangleCenter) circle(2.345cm);

    \begin{scope}[shift={(30:-2.309)}]
        \draw [line width=1.5pt, fill=gray!2] (0,0) -- (60:4) -- (4,0) -- cycle;
        \draw[thick, draw=green] (TriangleCenter) circle(1.12cm);
        \coordinate[label=left:$A$]  (A) at (0,0);
        \coordinate[label=right:$B$] (B) at (4,0);
        \coordinate[label=above:$C$] (C) at (2,3.464);


        % Sign for right angle of h_c
        %\begin{scope}[shift={(2,0)}]
        %    \draw[fill=gray!30] (0,0) -- node[above=-0.15cm,near start] {$\cdot$} (0:0.18cm)
        %                        arc (0:90:.18cm);
        %\end{scope}

        % sign of right angle of h_a
        %\begin{scope}[shift={(30:3.464cm)}]
        %    \draw[fill=gray!30] (0,0) -- node[near end,right=-0.28cm] {$\cdot$} (-60:0.18cm)
        %                        arc (-60:-150:.18cm);
        %\end{scope}

        % sign of right angle of h_b
        %\begin{scope}[shift={(60:2cm)}]
        %    \draw[fill=gray!30] (0,0) -- node[right=-0.08cm, near start] {$\cdot$} (60:0.18cm)
        %                        arc (60:-30:.18cm);
        %\end{scope}

        % angle alpha
        %\draw[fill=green!30] (0,0) -- (0:0.75cm) arc (0:60:.75cm);
        %\draw (0.35cm,0.25cm) node {$\alpha$};

        % angle beta
        \begin{scope}[shift={(4cm,0cm)}]
            %\draw[fill=green!30] (0,0) -- (-180:0.75cm) arc (180:120:0.75cm);
            \draw[color=gray, dashed] (0,0) -- node[sloped, above=-0.1cm] {} (150:3.464cm); % $\scriptstyle h_b$
            %\draw (150:0.5cm) node {$\beta$};
        \end{scope}

        % angle gamma
        \begin{scope}[shift={(60:4)}]
            %\draw[fill=green!30] (0,0) -- (-120:.75cm) arc (-120:-60:.75cm);
            \draw[color=gray, dashed] (0,0) -- node[right=-0.1cm] {} (-90:3.464cm); % $\scriptstyle h_c$
            %\draw (-90:0.5cm) node {$\gamma$};
        \end{scope}

        % Height with label
        \draw[color=gray, dashed] (0,0) -- node[sloped, above=-0.1cm] {} (30:3.464cm); % $\scriptstyle h_a$

        % The triangle
        \draw [line width=1.5pt] (0,0) -- (60:4) -- (4,0) -- cycle;
    \end{scope}

    \coordinate[label=below:$c$](c) at ($ (A)!.5!(B) $);
    \coordinate[label=left:$b$] (b) at ($ (A)!.5!(C) $);
    \coordinate[label=right:$a$](a) at ($ (B)!.5!(C) $);
  \end{tikzpicture}
\end{document}