\documentclass[a4paper]{article}
\usepackage{tkz-euclide}
\usetkzobj{all} 

\begin{document}

\begin{tikzpicture}
	\tkzDefPoint(1,2){A}
	\tkzDefPoint(3,4){B}
	\tkzDefPoint(2,4){C}
	\tkzCircumCenter(A,B,C)\tkzGetPoint{O}
	\tkzDrawArc(O,A)(C)
	\tkzDrawArc(O,C)(A)
	\foreach \p in {A,B,C,O}
		\fill[red] (\p) circle(2pt);
\end{tikzpicture}

\end{document}

% \documentclass[pstricks,border=3pt]{standalone}
% \usepackage{pst-eucl}

% \usepackage[T2A]{fontenc}
% \usepackage[russian,english]{babel}
% \usepackage[utf8]{inputenc}
% \usepackage{amsmath,amssymb}

% \begin{document}
% \pspicture(5,5)
%     \pstGeonode[PosAngle={-135,45,90}](1,2){A}(3,4){B}(2,4){C}
%     \pstCircleABC[DrawCirABC=false]{A}{B}{C}{O}
%     \pstArcnOAB{O}{A}{B}
% \endpspicture
% \end{document}

% \documentclass{article}

% \usepackage[T2A]{fontenc}
% \usepackage[russian,english]{babel}
% \usepackage[utf8]{inputenc}
% \usepackage{amsmath,amssymb}
% \usepackage{tikz}
% \usepackage{pst-eucl}
% \usetikzlibrary{calc}

% \newcommand{\arcThroughThreePoints}[4][]{
% 	\coordinate (middle1) at ($(#2)!.5!(#3)$);
% 	\coordinate (middle2) at ($(#3)!.5!(#4)$);
% 	\coordinate (aux1) at ($(middle1)!1!90:(#3)$);
% 	\coordinate (aux2) at ($(middle2)!1!90:(#4)$);
% 	\coordinate (center) at ($(intersection of middle1--aux1 and middle2--aux2)$);
% 	\draw[#1] 
% 	 let \p1=($(#2)-(center)$),
% 	      \p2=($(#4)-(center)$),
% 	      \n0={veclen(\p1)},    % Radius
% 	      \n1={atan2(\y1,\x1)}, % angles
% 	      \n2={atan2(\y2,\x2)},
% 	      \n3={\n2>\n1?\n2:\n2+360}
% 	    in (#2) arc(\n1:\n3:\n0);
% }

% \begin{document}

% \pagestyle{empty}

% \def\dx{7}
% \begin{tikzpicture}%[scale=3]
% 	\coordinate (A) at (3,1);
% 	\coordinate (B) at (1,2);
% 	\coordinate (C) at (-2,-2);
% 	% \coordinate (A) at (0,0);
% 	% \coordinate (B) at (1,2);
% 	% \coordinate (C) at (2,0);
% 	\arcThroughThreePoints{A}{B}{C};
% 	\foreach \p in {A,B,C,center}
% 		\fill[red] (\p) circle(2pt);

% \end{tikzpicture}

% \pspicture(5,5)
%     \pstGeonode[PosAngle={-135,45,90}](1,2){A}(3,4){B}(2,4){C}
%     \pstCircleABC[DrawCirABC=false]{A}{B}{C}{O}
%     \pstArcnOAB{O}{A}{B}
% \endpspicture

% \end{document}