[Tex/LaTex] How to draw a triangle is insribed in a circle so that the vertices divide the circle into three arcs of lengths 3, 4 and 5

Question

I want to draw a triangle circle is insribed in a circle so that the vertices divide the circle into three arcs of lengths 3, 4 and 5. I tried with Geogebra.

\documentclass[12pt]{standalone}
\usepackage{pgf,tikz}
\usepackage{mathrsfs}
\usetikzlibrary{arrows}
\pagestyle{empty}
\begin{document}
\begin{tikzpicture}[line cap=round,line join=round,>=triangle 45,x=1.0cm,y=1.0cm]
\clip(-0.5,-0.5) rectangle (4.5,4.298548095909735);
\draw(2.,2.) circle (2.cm);
\draw (0.64845913365678,3.4742242999639563)-- (0.5257757000360437,0.64845913365678);
\draw (0.5257757000360437,0.64845913365678)-- (3.907580874488035,1.3990547385264929);
\draw (3.907580874488035,1.3990547385264929)-- (0.64845913365678,3.4742242999639563);
\draw (-0.4,2.1844051666973288) node[anchor=north west] {3};
\draw (2.0939306358381504,0) node[anchor=north west] {4};
\draw (3,4.2) node[anchor=north west] {5};
\draw [fill=black] (2.,2.) circle (1.5pt);
\draw[color=black] (2,1.6) node {$I$};
\draw [fill=black] (0.64845913365678,3.4742242999639563) circle (1.5pt);
\draw[color=black] (0.6,3.8) node {$A$};
\draw [fill=black] (0.5257757000360437,0.64845913365678) circle (1.5pt);
\draw[color=black] (0.49,0.2) node {$B$};
\draw [fill=black] (3.907580874488035,1.3990547385264929) circle (1.5pt);
\draw[color=black] (4.15,1.377692733182069) node {$C$};
\end{tikzpicture}
\end{document}

How can I draw that picture by using tikz (or pstricks) with nice code?

Answer 1

Define a circle with 3+4+5=12 degrees:

\documentclass[pstricks]{standalone}
\usepackage{pstricks}
\begin{document}
\begin{pspicture}(-3,-3)(3,3)
\degrees[12]
\pspolygon[showpoints](2;1)(2;4)(2;8)
\pscircle[showpoints](0,0){2}
\uput[1](2;1){A}\uput[4](2;4){B}\uput[8](2;8){C}
\rput(1.7;2.5){3}\rput(1.5;6){4}\rput(1.25;11){5}
\end{pspicture}
\end{document}