\begin{tikzpicture}[scale=2]
                  \clip (-1.1,-1.1) rectangle (1.7,1.1);
                  \coordinate (o) at (0,0);
                  \coordinate (a) at (1,0);
                  \def\r{.65};
                  \tkzDefPoint(0:(1+\r^2)/(2*\r)){b}
                  \tkzDrawCircle[dashed,color=blue](o,a)
                  \foreach \x in {0,1,...,7} \tkzDefPoint(\x*45:\r){\x};
                  \tkzDefPoint(0:1/\r){vo*}
                  %\coordinate (vo) at (0:.8409);
                  \hypsegment{1}{0}{o}{a}
                  \hypsegment{2}{1}{o}{a}
                  \hypsegment{3}{2}{o}{a}
                  \hypsegment{4}{3}{o}{a}
                  \hypsegment{5}{4}{o}{a}
                  \hypsegment{6}{5}{o}{a}
                  \hypsegment{7}{6}{o}{a}
                  \hypsegment{0}{7}{o}{a}
                  \draw (o)--(vo*);
                  \draw[thin](1)--(0);
                  \draw[dashed,->](o)--(22.5:1.7);
                  \tkzDefLine[perpendicular=through b,K=.7](o,b)\tkzGetPoint{c}
                  \draw[dashed](b)--(c);
                  \tkzDefMidPoint(0,1)\tkzGetPoint{m}
                  \tkzInterLL(b,c)(o,m)\tkzGetPoint{zo}
                  \tkzDrawPoints[fill=red](o,0,1,2,3,4,5,6,7)
                  \tkzDrawPoints(b,vo*,m,zo)
                  \tkzLabelPoint[below right= 0pt and -2pt](b){\(b\)}
                  \tkzLabelPoint[below](vo*){\(v_o^*\)}
                  \tkzLabelPoint[below right=-2pt](0){\(v_0\)}
                  \tkzLabelPoint[above](1){\(v_1\)}
                  \tkzLabelPoint[above](2){\(v_2\)}
                  \tkzLabelPoint[left](3){\(v_3\)}
                  \tkzLabelPoint[left](4){\(v_4\)}
                  \tkzLabelPoint[below](5){\(v_5\)}
                  \tkzLabelPoint[below](6){\(v_6\)}
                  \tkzLabelPoint[below](7){\(v_7\)}
                  \tkzLabelPoint[right](zo){\(z_0\)}
\end{tikzpicture}