\begin{tikzpicture}[scale=2]
                    \clip (0,0) circle (1.25cm);
                    \coordinate (o) at (0,0);
                    \coordinate (r) at (1,0);
                    \coordinate (-1) at (-1,0);
                    \tkzDefPoint(70:.5){z}
                    \tkzDefPoint(-70:.5){zbar}
                    \tkzDefPoint(110:.5){w}
                    \tkzDefPoint(-110:.5){wbar}
                    \draw[dashed](-1)--(r);
                    \tkzCircumCenter(-1,z,r)\tkzGetPoint{c1}
                    \tkzDrawArc[dashed,color=black](c1,r)(-1)
                    \tkzCircumCenter(-1,zbar,r)\tkzGetPoint{c2}
                    \tkzDrawArc[dashed,color=black](c2,-1)(r)
                    \tkzDrawCircle[dashed,color=blue](o,r)
                    \tkzDefLine[perpendicular=through z,K=1](c1,z)\tkzGetPoint{pt};
                    \tkzInterLL(z,pt)(-1,r)\tkzGetPoint{l1}
                    \tkzInterCC(l1,z)(o,r)\tkzGetPoints{t1}{t2}
                    \tkzDrawArc[dashed,color=black](l1,t2)(t1)
                    \tkzCircumCenter(-1,w,r)\tkzGetPoint{d1}
                    \tkzDefLine[perpendicular=through w,K=1](d1,w)\tkzGetPoint{pt2};
                    \tkzInterLL(w,pt2)(-1,r)\tkzGetPoint{l2}
                    \tkzInterCC(l2,w)(o,r)\tkzGetPoints{tw1}{tw2}
                    \tkzDrawArc[dashed,color=black](l2,tw2)(tw1)
                    \fill[fill=blue,opacity=0.1] (w) to [bend left=8]  (wbar) to [bend right=5] 
                    (zbar) to [bend left=8] (z) to [bend right=5] (w);
                    \tkzDrawArc[color=blue](l2,wbar)(w)
                    \tkzDrawArc[color=blue](l1,z)(zbar)
                    \tkzDrawArc[color=blue](c1,z)(w)
                    \tkzDrawArc[color=blue](c2,wbar)(zbar)
                    \tkzInterLC(o,r)(l1,z)\tkzGetPoints{a}{a1}
                    \tkzInterLC(o,r)(l2,w)\tkzGetPoints{am1}{am}
                    \tkzDrawPoints[fill=red](z,a)
                    \tkzDrawPoints(zbar,-1,r,w,wbar,am)
                    \tkzLabelPoint[right](r){\(1\)}
                    \tkzLabelPoint[left](-1){\(-1\)}
                    \tkzLabelPoint[above right](z){\(z\)}
                    \tkzLabelPoint[below right](zbar){\(\overline{z}\)}
                    \tkzLabelPoint[below right](a){\(a\)}
                    \tkzLabelPoint[below left=-2pt](am){\(-a\)}
                    \draw (75:1.1) node{\(L_1\)};
                    \draw (105:1.1) node{\(L_2\)};
                    \draw (30:.84) node{\(C_1\)};
                    \draw (-30:.84) node{\(C_2\)};
\end{tikzpicture}