I want to draw and label angle A (alpha) of my ABC triangle while still being able to change to coordinate of A B and C so that the angle and the mark adapts to it.

\documentclass{article}
\usepackage{pgfplots}
\usetkzobj{all} %also needed
\begin{document}
\begin{tikzpicture}
\coordinate (M) at (0,0) ;
\coordinate (A) at (canvas polar cs:angle=90,radius=3cm) ;
\coordinate (B) at (canvas polar cs:angle=-30,radius=3cm) ;
\coordinate (C) at (canvas polar cs:angle=30,radius=3cm);
\draw (M) circle (3cm);
\draw (A) -- (B) -- (C) --cycle;
\tkzDrawPoints(A,B,C,M);
\tkzLabelPoints[above](A,C);
\tkzLabelPoints(B,M);
\tkzMarkAngle[fill= red,size=1.5cm, opacity=.4](B,A,C); %thanks to Claudio
\tkzLabelAngle[pos = 0.8](B,A,C){$\alpha$};
\end{tikzpicture}
\end{document}
tkz-euclide. It's the best tool for such constructions – percusse Aug 24 '13 at 12:20