\input{../Triangle.tikz}
\tikzmath{\a=1;};
\tikzmath{\b=3;};
\tikzmath{\c=2;};


\coordinate (O) at (0,0);
\coordinate (P1) at (-\a,0);
\coordinate (P2) at (\b,0);
\coordinate (P3) at (0,\c);
   
\DrawPoint{(P1)}{P_1}{anchor=north east};
\DrawPoint{(P2)}{P_2}{anchor=north west};
\DrawPoint{(P3)}{P_3}{anchor=south east};
   
\DrawTriangle{(P1)}{(P2)}{(P3)};
\DrawTriangleCircumCenter{(P1)}{(P2)}{(P3)};
\DrawTriangleMediatrizes{(P1)}{(P2)}{(P3)};



\coordinate (Q1) at ($(P2)-(P1)$);
\coordinate (Q2) at ($(P3)-(P1)$);
\coordinate (Q12) at ($(Q2)-(Q1)$);

\gettikzxy{(Q1)}{\vx}{\vy};
\gettikzxy{(Q2)}{\wx}{\wy};
\gettikzxy{(Q12)}{\ux}{\uy};

\tikzmath{\Det=\vx*\wy-\vy*\wx;};
\tikzmath{\R=sqrt(\vx*\vx+\vy*\vy);};
\tikzmath{\RR=sqrt(\wx*\wx+\wy*\wy);};
\tikzmath{\RRR=sqrt(\ux*\ux+\uy*\uy);};

%\draw[color=lightgray] (P1) circle(\R);
%\draw[color=lightgray] (P1) circle(\RR);
%\draw[color=lightgray] (P2) circle(\RRR);

\tikzmath{\r=0.5/\Det*\R*\RR*\RRR;};


\draw[color=lightgray] (Circum) circle(\r);

\tkzLabelSegment[below](P1,P2) {\small{$r_{12}$}};
\tkzLabelSegment[left](P1,P3) {\small{$r_{13}$}};
\tkzLabelSegment[above](P2,P3) {\small{$r_{23}$}};