\begin{tikzpicture}[scale=2,extended line/.style={shorten >=-#1,shorten <=-#1},extended line/.default=2cm]
            \tikzset{mwe/.style={inner sep=.6ex, text depth=0ex, text height=2ex, text width=.3em, minimum size = 0.5em}}
            \tkzDefPoint(0,0){o}
            \tkzDefPoint(1,0){a}
            \tkzDefPoint(-10:.6){z}
            \tkzDefPoint(-10:1.667){zstar}
            \tkzDefPoint(45:1){w1}
            \tkzDefPoint(300:1){w2}
            \tkzDefCircle[orthogonal through=z and w1](o,a) \tkzGetPoint{c1}
            \tkzDefCircle[orthogonal through=z and w2](o,a) \tkzGetPoint{c2}
            \tkzDefMidPoint(z,zstar)\tkzGetPoint{m}
            \tkzDrawCircle[color=blue](o,a)
            \tkzDrawCircle[thin](c1,z)
            \tkzDrawCircle[thin](c2,z)
            \tkzDrawLine[dashed](c1,z)
            \tkzDrawLine[dashed](c2,z)
            \tkzDefLine[perpendicular=through z,K=-2.3](z,c1)
            \tkzGetPoint{l2};
            \tkzDefLine[perpendicular=through z,K=2.3](z,c2)
            \tkzGetPoint{l1};
            \draw(z)--(l1) node[right]{\(L_1\)};
            \draw(z)--(l2) node[right]{\(L_2\)};
            \tkzDrawSegment(z,l2)
            \draw (115:1.1) node{\(C\)};
            \draw (340:1.95) node{\(C_1\)};
            \draw (5:2.05) node{\(C_2\)};
            \draw (100:.7) node{\(m_1\)};
            \draw (240:.5) node{\(m_2\)};
            \draw (45:1.7) node{\(k\)};
            \draw[extended line, dashed, <->] (c1)--(c2);
            \draw[extended line, dashed,<->](z)--(c1);
            \draw[extended line, dashed,<->](z)--(c2);
            \draw[color=blue,thick,->] (z)++(40:.15) arc(40:-55:.15cm);
            \draw[color=blue,thick,->] (zstar)++(120:.15) arc(120:215:.15cm);
            \tkzDrawPoints[fill=red](z,zstar)
            \tkzDrawPoints[fill=red](o,m,c1,c2)
            \tkzLabelPoint[left](z){\(z\)}
            \tkzLabelPoint[right](zstar){\(z^*\)}
            \end{tikzpicture}