Q:

How to draw a clip inside circle TikZ?

I looking for drawing some forms with Tikz using the following code :
\begin{figure}
\centering

\shade[ball color=gray] (0,4) circle (5ex);
\shade[ball color=black] (1,4) circle (5ex);

\shade[ball color=gray] (7,4) circle (5ex);
\shade[ball color=black] (9,4) circle (5ex);

\shade[ball color=gray] (4,1) circle (5ex);
\shade[ball color=black] (5,1) circle (5ex);
\shade[ball color=gray!70] (4.5,0) circle (5ex);
\end{tikzpicture}

\label{fig1chap3}

\end{figure}

but I cannot figure out how to draw the framed forms as the following picture :

A:

Clipping can helping here a lot, a starting point:
\documentclass{article}
\usepackage{tikz}
\begin{document}
\begin{tikzpicture}[
  radius=10mm,
]
  \begin{scope}
    \clip (0, 0) circle;
    \fill[red] (0, 0) circle;
    \fill[red!50!blue, overlay] (13mm, 0) circle;
  \end{scope}
\end{tikzpicture}
\end{document}

\documentclass{article}
\usepackage{tikz}
\begin{document}
\begin{tikzpicture}[
  radius=10mm,
]
  \begin{scope}[even odd rule]
    \clip[overlay]
      (-11mm, -11mm) rectangle (11mm, 11mm)
      (13mm, 0) circle;
    \fill[red] (0, 0) circle;
  \end{scope}
  \begin{scope}[xshift=4mm]
    \clip (0, 0) circle;
    \clip (13mm, 0) circle;
    \fill[red!50!blue] (0, 0) circle;
  \end{scope}
  \begin{scope}[xshift=8mm, even odd rule]
    \clip[overlay]
      (13mm - 11mm, -11mm) rectangle (13mm + 11mm, 11mm)
      (0, 0) circle;
    \fill[blue] (13mm, 0) circle;
  \end{scope}
\end{tikzpicture}
\end{document}

Using two circles for clipping for the left or right side of the previous drawing will not work:
\begin{scope}[even odd rule]
  \clip (0, 0) circle[]
        (13mm, 0) circle;
  \fill[red] (0, 0) circle;
\end{scope}

The problem is the border of the first circle in the area of the second circle. There, the circle is drawn with a faint line. The problem is worked
around by using a larger area for the first circle.
With shading
\documentclass{article}
\usepackage{tikz}
\begin{document}
\begin{tikzpicture}[
  radius=10mm,
]
  \begin{scope}[even odd rule]
    \clip[overlay]
      (-11mm, -11mm) rectangle (11mm, 11mm)
      (13mm, 0) circle[];
    ;
    \fill[shading=ball, ball color=red] (0, 0) circle;
  \end{scope}
  \begin{scope}[xshift=4mm]
    \clip (0, 0) circle;
    \clip (13mm, 0) circle;
    \fill[shading=ball, ball color=red!50!blue] (0, 0) circle;
  \end{scope}
  \begin{scope}[xshift=8mm, even odd rule]
    \clip[overlay]
      (13mm - 11mm, -11mm) rectangle (13mm + 11mm, 11mm)
      (0, 0) circle;
    \fill[shading=ball, ball color=blue] (13mm, 0) circle;
  \end{scope}
\end{tikzpicture}
\end{document}

