tkz-euclide fill parts of a circle

Question

I'm currently able to draw this image with the following code:

\documentclass[tikz,border=3mm]{standalone}
\begin{document}
\begin{tikzpicture}
    \tkzInit[xmax=3,ymax=3,xmin=-3,ymin=-3]
    \tkzGrid
    \tkzAxeXY
    \tkzDefPoint(0,0){A}
    \tkzDefPoint(1,0){B}
    \tkzDefPoint(2,0){C}
    \tkzDefCircle[through](A,B)
    \tkzDefCircle[through](A,C)
    \tkzDrawCircle[color=red](A,C)
    \tkzDrawCircle[color=red](A,B)
\end{tikzpicture}
\end{document}

And I want to fill parts of the outer circle, but it shouldn't overwrite the inner circle. Basically like this:

How could I do this with tkz-euclide or any other tikz library?

Answer 1

I am not too familiar with tkz-euclide but with just TikZ it is very easy.

\documentclass[tikz,border=3mm]{standalone}
\begin{document}
\begin{tikzpicture}
\begin{scope}
 \clip (0,-3) -| (-3,0) -| (3,3) -| cycle;
 \fill[gray,even odd rule] circle[radius=2] circle[radius=1];
\end{scope}
\draw[red]  circle[radius=2] circle[radius=1];
\end{tikzpicture}
\end{document}