how to fill intersection of 2 shapes in latex tikz package

Question

I have to fill a specific region as given in the following figure.

The code I have written is

\begin{tikzpicture}

\draw (0,0) rectangle (10,10);

\draw (3.5,3.5) circle (5) node {A};

\end{tikzpicture}

Now, how to fill the intersecting area (area of circle overlapping the square)

Answer 1

Use clipping, e.g. like this

\documentclass{article}
\usepackage{tikz}

\begin{document}
\begin{tikzpicture}
\begin{scope}
  \clip (0,0) rectangle (10,10);
  \fill[red] (3.5,3.5) circle (5);
\end{scope}
\draw (0,0) rectangle (10,10);
\draw (3.5,3.5) circle (5) node {A};
\end{tikzpicture}
\end{document}