\begin{tikzpicture} \begin{scope} \tkzDefPoint(0,0){o} \tkzDefPoint(2,0){a} \tkzDefPoint(40:1.3){p} \tkzDefPoint(40:4/1.3){p*} \tkzDefPoint(90:1){v1} \tkzDefPoint(270:.8){v2} \tkzDefPoint(240:1.6){v3} \tkzLabelPoint(p){\(p\)} \draw (110:2.2) node{\(L_1\)}; \draw(255:2.3) node{\(L_2\)}; \tkzClipCircle(o,a) \tkzDefCircle[orthogonal through=v1 and p](o,a)\tkzGetPoint{c1} \tkzDrawCircle(c1,p) \tkzDefCircle[orthogonal through=v2 and p](o,a)\tkzGetPoint{c2} \tkzDrawCircle(c2,p) \tkzDefPoint(.2,1.66){z} \tkzLabelPoint[below](z){\(z\)} \tkzDefPointBy[inversion = center c1 through p](z)\tkzGetPoint{z*} \tkzLabelPoint[left](z*){\(z^\prime\)} \tkzDefPointBy[inversion = center c2 through p](z*)\tkzGetPoint{Tz} \tkzDrawCircle[dashed,draw=blue](o,a) \typeIIcline[thin, dashed]{p}{p*}{v1} \typeIIcline[thin, dashed]{p}{p*}{v2} \typeIIcline[thin, dashed]{p}{p*}{v3} \tkzDrawPoint[size=8](z*) \tkzDrawPoints[size=8,fill=red](p,z,Tz) \tkzLabelPoint[below](Tz){\(T(z)\)} \end{scope} \begin{scope}[xshift=6cm] \clip(0,0) circle (2.6cm); \tkzDefPoint(0,0){o} \tkzDefPoint(2,0){a} \tkzDefPoint(200:2){p} \tkzDefPoint(200:1.6){v1} \tkzDefPoint(200:1.1){v2} \tkzDefPoint(200:.5){v3} \tkzDrawCircle[thin, dashed](v1,p) \tkzDrawCircle[thin, dashed](v2,p) \tkzDrawCircle[thin, dashed](v3,p) \tkzDefPoint(90:1){x} \tkzDefPoint(270:.8){y} \tkzDrawCircle[dashed,draw=blue](o,a) \tkzLabelPoint[left](p){\(p\)} \tkzDefPoint(.66,.8){z} \draw (80:2.2) node{\(L_1\)}; \draw(300:2.3) node{\(L_2\)}; \tkzDrawPoint[size=8,fill=red](z) \tkzDrawPoint[size=8,fill=white](p) \tkzLabelPoint[below](z){\(z\)} \tkzClipCircle(o,a) \tkzDefCircle[orthogonal through=x and p](o,a)\tkzGetPoint{c1} \tkzDrawCircle(c1,x) \tkzDefCircle[orthogonal through=y and p](o,a)\tkzGetPoint{c2} \tkzDrawCircle(c2,y) \tkzDefPointBy[inversion = center c1 through p](z)\tkzGetPoint{z*} \tkzDrawPoint[size=8](z*) \tkzLabelPoint[above](z*){\(z^\prime\)} \tkzDefPointBy[inversion = center c2 through p](z*)\tkzGetPoint{Tz} \tkzDrawPoints[size=8,fill=red](Tz) \tkzDrawPoint[size=8,fill=white](p) \tkzLabelPoint[above right=-5pt](Tz){\(T(z)\)} \draw (0,-2.4) node{(b)}; \end{scope} \begin{scope}[xshift=3cm,yshift=-4.8cm] \clip(0,0) circle (2.6cm); \tkzDefPoint(0,0){o} \tkzDefPoint(2,0){a} \tkzDefPoint(80:2){p} \tkzDefPoint(330:2){q} \tkzLabelPoint[above](p){\(p\)} \tkzLabelPoint[right](q){\(q\)} \tkzDefPoint(180:.8){v1} \tkzDefPoint(0,.5){v2} \tkzDefPoint(30:1.7){v3} \tkzDefPoint(90:.5){u1} \tkzDefPoint(270:1){u2} \tkzDrawCircle[dashed,draw=blue](o,a) \tkzDrawSegment[thin, dashed](p,q) \arcThroughThreePoints[thin, dashed,color=black]{p}{v1}{q}; \arcThroughThreePoints[thin, dashed,color=black]{p}{v2}{q}; \arcThroughThreePoints[thin, dashed,color=black]{q}{v3}{p}; \tkzDefPoint(91.5:1){z} \tkzDrawPoints[size=8,fill=red](z,p,q) \tkzDrawPoints[size=8,fill=white](p,q) \draw (35:2.3) node{\(L_1\)}; \draw(8:2.3) node{\(L_2\)}; \tkzClipCircle(o,a) \typeIIcline{p}{q}{u1}\tkzGetPoint{c1} \typeIIcline{p}{q}{u2}\tkzGetPoint{c2} \tkzLabelPoint[right](z){\(z\)} \tkzDefPointBy[inversion = center c1 through u1](z)\tkzGetPoint{z*} \tkzDrawPoint[size=8](z*) \tkzLabelPoint[right](z*){\(z^\prime\)} \tkzDefPointBy[inversion = center c2 through u2](z*)\tkzGetPoint{Tz} \tkzDrawPoints[size=8,fill=red](Tz) \tkzLabelPoint[above right=-5pt](Tz){\(T(z)\)} \end{scope} \begin{scope}[yshift=-.8cm] \draw (0,-1.8) node{(a)}; \draw (6,-1.8) node{(b)}; \draw (3,-6.5) node{(c)}; \end{scope} \end{tikzpicture}