\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}