\begin{tikzpicture}\draw[blue] (0,0) circle (2cm);
\draw (1,-2) node{$$C$$};
\fill[color=red] (0,0) circle (1pt) node[color=black,below]{$$z_0$$};
\coordinate (A) at (.865,2.811);
\coordinate (B) at (0,3.077);
\coordinate (C) at (-.865,2.811);
\arcThroughThreePoints{A}B{C};
\coordinate (A) at (.664,2.49);
\coordinate (B) at (0,2.667);
\coordinate (C) at (-.664,2.49);
\arcThroughThreePoints{A}B{C};
\coordinate (A) at (.525,2.23);
\coordinate (B) at (0,2.353);
\coordinate (C) at (-.525,2.23);
\arcThroughThreePoints{A}B{C};
\draw (0,3.077)--(0,2.353);
\coordinate (A) at (-.525,2.23);
\coordinate (B) at (-.664,2.49);
\coordinate (C) at (-.865,2.811);
\arcThroughThreePoints{A}B{C};
\coordinate (A) at (.865,2.811);
\coordinate (B) at (.664,2.49);
\coordinate (C) at (.525,2.23);
\arcThroughThreePoints{A}B{C};
\draw (-.4,1.3) rectangle (.4,1.7);
\draw (-.4,1.5) -- (.4,1.5) (0,1.3)--(0,1.7);
\foreach \x in {-.4,0,.4}
\foreach \y in {1.3,1.5,1.7}
{
\fill[color=red](\x,\y) circle (1pt);
\pgfmathsetmacro\p{4*\x/(\x*\x +\y*\y)}
\pgfmathsetmacro\q{4*\y/(\x*\x +\y*\y)}
\fill[color=red](\x,\y) circle (1pt);
\fill[color=blue] (\p,\q) circle (1pt);
}
\draw (1.2,-.3)--(1.2,.3)--(1.5,0)--(1.8,.3)--(1.8,-.3);
\coordinate (A) at (3.137,-.784);
\coordinate (B) at (3.333,0);
\coordinate (C) at (3.137,.784);
\arcThroughThreePoints{A}B{C};
\coordinate (A) at (2.162,-.36);
\coordinate (B) at (2.222,0);
\coordinate (C) at (2.162,.36);
\arcThroughThreePoints{A}B{C};
\coordinate (A) at (2.667,0);
\coordinate (B) at (2.927,.325);
\coordinate (C) at (3.147,.784);
\arcThroughThreePoints{A}B{C};
\coordinate (A) at (2.667,0);
\coordinate (B) at (2.404,.219);
\coordinate (C) at (2.162,.36);
\arcThroughThreePoints{A}B{C};
\foreach \x in {1.2,1.8}
\foreach \y in {-.3,0,.3}
{
\fill[color=red](\x,\y) circle (1pt);
\pgfmathsetmacro\p{4*\x/(\x*\x +\y*\y)}
\pgfmathsetmacro\q{4*\y/(\x*\x +\y*\y)}
\fill[color=red](\x,\y) circle (1pt);
\fill[color=blue] (\p,\q) circle (1pt);
}
\fill[color=red](1.5,0) circle (1pt);
\fill[color=blue](4/1.5,0) circle (1pt);

\coordinate (A) at (140:1.7);
\coordinate (B) at (150:1.8);
\coordinate (C) at (160:1.6);
\arcThroughThreePoints{A}B{C};
\arcThroughThreePoints{C}B{A};

\foreach \p in {A,B,C}
\fill[red] (\p) circle(1pt);

\coordinate (D) at (140:4/1.7);
\coordinate (E) at (150:4/1.8);
\coordinate (F) at (160:4/1.6);
\arcThroughThreePoints{D}E{F};
\arcThroughThreePoints{F}E{D};

\foreach \q in {D,E,F}
\fill[blue] (\q) circle(1pt);

\draw (160:1.6) node[below]{$$p$$};
\draw (160:4/1.6) node[below]{$$i_C(p)$$};
\draw (1.2,.3) node[above]{$$v$$};
\draw (1.8,-.3) node[below]{$$u$$};
\draw (3.5,.7) node[above]{$$i_C(v)$$};
\draw (2.4,-.56) node{$$i_C(u)$$};
\draw (-.4,1.3) node[below]{$$z$$};
\draw (.4,1.7) node[right]{$$w$$};
\draw (-1,2.8) node[above]{$$i_C(z)$$};
\draw (1,2.2) node{$$i_C(w)$$};
\end{tikzpicture}