Drawing a triangle with smooth curves in the middle

This is a solution where the starting angle=15 deg (with radius=1.5cm) and ending angle=45 deg for the pie inside. As to the sector region, the radii are 2.5cm and 4cm respectively. These all can be changed to suit one's need.

The syntax for drawing an arc can be done via

\draw (x,y) arc (alph:beta:r);     % where x+jy=r\angle alph
\draw (alph:r) arc (alph:beta:r);  % start angle=alpha, end angle=beta, radius=r.

Code

\documentclass[border=10pt]{standalone}
\usepackage{tikz}
\usetikzlibrary{positioning,intersections}


\begin{document}

\begin{tikzpicture}
\draw (-2.5,0)node[left]{-1}--(2.5,0) node[right]{1};
\draw (0,2.5) node[right]{1}--(0,-2.5)node[right]{-1};
\draw (0,0) circle (2cm);
\draw (0,0) -- +(15:1.5cm) arc (15:45:1.5cm) -- cycle;
\draw (15:2.5)--(15:4) arc (15:45:4) --node[left]{$\bar T$} (45:2.5) arc (45:15:2.5);
\draw (25:1.5)--node[pos=0.2,above]{$\epsilon$}
                node[pos=0.7,above]{$\epsilon$}(25:2.5);
\end{tikzpicture}


\end{document}

Run with xelatex or latex->dvips->ps2pdf

\documentclass{article}
\usepackage{pstricks-add}
\begin{document}

\psset{unit = 2}
\begin{pspicture}(-1.7,-1.7)(2,2)
  \psaxes[xlabelsep =-0.02,xlabelOffset = 0.07,
          ylabelsep = -0.02,ylabelOffset = 0.1,
          arrowscale=1.5,linewidth=0.5pt]{->}(0,0)(-1.7,-1.7)(2,2)
  \pscircle(0,0){1}
  \psset{origin={0.15,0.05}}
  \pswedge[fillcolor=black!10,fillstyle=solid](0,0){0.65}{0}{30}
  \pscustom[fillcolor=black!10,fillstyle=solid]{
    \psline(1.05;30)(1.5;30)(1.5,0)
    \psarc(0,0){1.05}{0}{30}}  
  \pcline(0.8;20)(1.2;20)
  \naput[npos=0.2]{\small $\epsilon$}
  \naput[npos=0.8]{\small $\epsilon$}
  \naput[npos=1.5,labelsep=0.2]{\small $\overline{T}$}
\end{pspicture}

\end{document}

Just another solution with PSTricks.

\documentclass[pstricks,border=12pt,12pt]{standalone}
\usepackage{pst-eucl}
\psset{unit=2,PointSymbol=none,linejoin=1}
\begin{document}
\multido{\i=15+5}{15}{%
\begin{pspicture}(-1.5,-1.5)(2,1.5)
    \pstGeonode[PosAngle={-135,-45,-135,135},PointName={-1,1,-1,1}](-1,0){A}(1,0){B}(0,-1){C}(0,1){D}
    \pcline[nodesep=-.5](A)(B)
    \pcline[nodesep=-.5](C)(D)
    \pscircle{1}
    \def\temp{%
        \pnodes(0,0){O}(1.5;10){P}(1.5;\i){Q}%
        \pswedge{.5}{(P)}{(Q)}%
        \pscustom{\psarc(O){1}{(P)}{(Q)}\psline(Q)(P)\closepath}%
        \pstBissectBAC[linestyle=none,PointName=none]{P}{O}{Q}{R}%
        \pnodes([nodesep=.5]{R}O){X}([nodesep=1]{R}O){Y}%
        \pcline(X)(Y)%
        \psset{labelsep=2pt}
        \naput[npos=.2]{$\epsilon$}%
        \naput[npos=.8]{$\epsilon$}%
        \pcline[linestyle=none]([nodesep=1]{Q}O)(Q)%
        \naput{$\overline{T}$}%
    }%
    \rput(.3;10){\temp}
\end{pspicture}}

\end{document}