\begin{tikzpicture} \begin{scope} \clip(0,0) circle (2.5cm); \tkzDefPoint(0,0){o} \tkzDefPoint(2,0){a} \tkzDrawCircle[thin, dashed,color=blue](o,a) \tkzDefPoint(250:.8){p} \tkzDefPoint(250:4/.8){p*} \tkzDefPoint(175:1.8){ghost1}%%sets the line L1 \tkzDefPoint(225:1.8){ghost2}%% sets the Line L2 \tkzCircumCenter(p,p*,ghost1)\tkzGetPoint{c1}% Center of L1 \tkzCircumCenter(p,p*,ghost2)\tkzGetPoint{c2}% Center of L2 \tkzInterCC(o,a)(c1,p)\tkzGetPoints{u1}{v1} \tkzInterCC(o,a)(c2,p)\tkzGetPoints{u2}{v2} \tkzDrawArc[color=black](c1,u1)(v1) \tkzDrawArc[color=black](c2,u2)(v2) \tkzDefPoint(248:1.7){z}\tkzDefPoint(248:4/1.7){z*} %%%% Drawing the M \tkzDefPoint(248:1.4){m}\tkzDefPoint(248:4/1.4){m*} \tkzDefPoint(255:1.6){n} \tkzDefPoint(260:1.3){w}\tkzDefPoint(260:4/1.3){w*} \tkzDefPoint(260:1.7){t} \draw[thick,color=blue] (z)--(m) (w)--(t); \tkzCircumCenter(m,m*,n)\tkzGetPoint{cm}; \tkzDrawArc[thick,color=blue](cm,n)(m); \tkzCircumCenter(n,w,w*)\tkzGetPoint{cw}; \tkzDrawArc[thick,color=blue](cw,w)(n); %%%% Reflecting corners of M across L1 \tkzDefPointBy[inversion = center c1 through p](z)\tkzGetPoint{z1} \tkzDefPointBy[inversion = center c1 through p](m)\tkzGetPoint{m1} \tkzDefPointBy[inversion = center c1 through p](n)\tkzGetPoint{n1} \tkzDefPointBy[inversion = center c1 through p](w)\tkzGetPoint{w1} \tkzDefPointBy[inversion = center c1 through p](t)\tkzGetPoint{t1} %%% Reflecting these images across L2 to get T(points) \tkzDefPointBy[inversion = center c2 through p](z1)\tkzGetPoint{z2} \tkzDefPointBy[inversion = center c2 through p](m1)\tkzGetPoint{m2} \tkzDefPointBy[inversion = center c2 through p](n1)\tkzGetPoint{n2} \tkzDefPointBy[inversion = center c2 through p](w1)\tkzGetPoint{w2} \tkzDefPointBy[inversion = center c2 through p](t1)\tkzGetPoint{t2} %%% Reflecting the points2 across L1 \tkzDefPointBy[inversion = center c1 through p](z2)\tkzGetPoint{z3} \tkzDefPointBy[inversion = center c1 through p](m2)\tkzGetPoint{m3} \tkzDefPointBy[inversion = center c1 through p](n2)\tkzGetPoint{n3} \tkzDefPointBy[inversion = center c1 through p](w2)\tkzGetPoint{w3} \tkzDefPointBy[inversion = center c1 through p](t2)\tkzGetPoint{t3} %%% Reflecting the points3 across L2 \tkzDefPointBy[inversion = center c2 through p](z3)\tkzGetPoint{z4} \tkzDefPointBy[inversion = center c2 through p](m3)\tkzGetPoint{m4} \tkzDefPointBy[inversion = center c2 through p](n3)\tkzGetPoint{n4} \tkzDefPointBy[inversion = center c2 through p](w3)\tkzGetPoint{w4} \tkzDefPointBy[inversion = center c2 through p](t3)\tkzGetPoint{t4} %%% Drawing T(M) \tkzDefPointBy[inversion = center o through a](m2)\tkzGetPoint{m2*} \tkzDefPointBy[inversion = center o through a](w2)\tkzGetPoint{w2*} \tkzCircumCenter(z2,m2,m2*)\tkzGetPoint{Tcz}; \tkzDrawArc[thick,color=blue](Tcz,z2)(m2); \tkzCircumCenter(m2,m2*,n2)\tkzGetPoint{Tcn}; \tkzDrawArc[thick,color=blue](Tcn,n2)(m2); \tkzCircumCenter(n2,w2,w2*)\tkzGetPoint{Tcw}; \tkzDrawArc[thick,color=blue](Tcw,n2)(w2); \tkzCircumCenter(t2,w2*,w2)\tkzGetPoint{Tct}; \tkzDrawArc[thick,color=blue](Tct,t2)(w2); %%% Drawing T(T(M)) \tkzDefPointBy[inversion = center o through a](m4)\tkzGetPoint{m4*} \tkzDefPointBy[inversion = center o through a](w4)\tkzGetPoint{w4*} \tkzCircumCenter(z4,m4,m4*)\tkzGetPoint{Tcz4}; \tkzDrawArc[thick,color=blue](Tcz4,m4)(z4); \tkzCircumCenter(m4,m4*,n4)\tkzGetPoint{Tcn4}; \tkzDrawArc[thick,color=blue](Tcn4,n4)(m4); \tkzCircumCenter(n4,w4,w4*)\tkzGetPoint{Tcw4}; \tkzDrawArc[thick,color=blue](Tcw4,w4)(n4); \tkzCircumCenter(t4,w4*,w4)\tkzGetPoint{Tct4}; \tkzDrawArc[thick,color=blue](Tct4,w4)(t4); %%%% Lines of Motion \tkzCircumCenter(p,p*,z)\tkzGetPoint{cpz} \tkzDefLine[perpendicular=through z,K=1](cpz,z)\tkzGetPoint{vz}; \tkzInterLL(z,vz)(p,p*)\tkzGetPoint{centerz} \tkzDrawCircle[very thin, dashed](centerz,z) \tkzCircumCenter(p,p*,w)\tkzGetPoint{cpw} \tkzDefLine[perpendicular=through w,K=1](cpw,w)\tkzGetPoint{vw}; \tkzInterLL(w,vw)(p,p*)\tkzGetPoint{centerw} \tkzDrawCircle[very thin, dashed](centerw,w) \tkzDrawPoints[fill=blue](w,w2,w4) \tkzDrawPoints[size=8,fill=red](z,z2,z4) \tkzLabelPoint[above](p){\(p\)} \tkzLabelPoint[below](z){\(z\)} \tkzLabelPoint[right](z2){\(T(z)\)} \tkzLabelPoint[left = -2pt](z4){\(T^2(z)\)} \draw (175:2.3) node{\(L_1\)}; \draw (225:2.3) node{\(L_2\)}; \tkzDrawPoint[size=12,fill=red](p) \end{scope} \begin{scope}[xshift=6cm] \clip(0,0) circle (2.5cm); \tkzDefPoint(0,0){o} \tkzDefPoint(2,0){a} \tkzDrawCircle[thin, dashed,color=blue](o,a) \tkzDefPoint(280:2){p} \tkzDefPoint(60:2){q} \tkzDefPoint(270:1.1){ghost1}%%point on line L1 \tkzDefPoint(270:.5){ghost2}%% point on Line L2 \tkzCircumCenter(p,q,ghost1)\tkzGetPoint{cg1} \tkzDefLine[perpendicular=through ghost1,K=1](cg1,ghost1)\tkzGetPoint{g1}; \tkzInterLL(ghost1,g1)(p,q)\tkzGetPoint{c1} \tkzInterCC(c1,ghost1)(o,a)\tkzGetPoints{v1}{u1} \tkzDrawArc[color=black](c1,u1)(v1) \tkzCircumCenter(p,q,ghost2)\tkzGetPoint{cg2} \tkzDefLine[perpendicular=through ghost2,K=1](cg2,ghost2)\tkzGetPoint{g2}; \tkzInterLL(ghost2,g2)(p,q)\tkzGetPoint{c2} \tkzInterCC(c2,ghost2)(o,a)\tkzGetPoints{v2}{u2} \tkzDrawArc[color=black](c2,u2)(v2) \tkzDrawPoints(p,q) \tkzDefPoint(248:1.7){z}\tkzDefPoint(248:4/1.7){z*} %%%% Drawing the M \tkzDefPoint(248:1.4){m}\tkzDefPoint(248:4/1.4){m*} \tkzDefPoint(255:1.6){n} \tkzDefPoint(260:1.3){w}\tkzDefPoint(260:4/1.3){w*} \tkzDefPoint(260:1.7){t} \draw[thick,color=blue] (z)--(m) (w)--(t); \tkzCircumCenter(m,m*,n)\tkzGetPoint{cm}; \tkzDrawArc[thick,color=blue](cm,n)(m); \tkzCircumCenter(n,w,w*)\tkzGetPoint{cw}; \tkzDrawArc[thick,color=blue](cw,w)(n); %%%% Reflecting corners of M across L1 \tkzDefPointBy[inversion = center c1 through ghost1](z)\tkzGetPoint{z1} \tkzDefPointBy[inversion = center c1 through ghost1](m)\tkzGetPoint{m1} \tkzDefPointBy[inversion = center c1 through ghost1](n)\tkzGetPoint{n1} \tkzDefPointBy[inversion = center c1 through ghost1](w)\tkzGetPoint{w1} \tkzDefPointBy[inversion = center c1 through ghost1](t)\tkzGetPoint{t1} %%% Reflecting these images across L2 to get T(points) \tkzDefPointBy[inversion = center c2 through ghost2](z1)\tkzGetPoint{z2} \tkzDefPointBy[inversion = center c2 through ghost2](m1)\tkzGetPoint{m2} \tkzDefPointBy[inversion = center c2 through ghost2](n1)\tkzGetPoint{n2} \tkzDefPointBy[inversion = center c2 through ghost2](w1)\tkzGetPoint{w2} \tkzDefPointBy[inversion = center c2 through ghost2](t1)\tkzGetPoint{t2} %%% Reflecting the points2 across L1 \tkzDefPointBy[inversion = center c1 through ghost1](z2)\tkzGetPoint{z3} \tkzDefPointBy[inversion = center c1 through ghost1](m2)\tkzGetPoint{m3} \tkzDefPointBy[inversion = center c1 through ghost1](n2)\tkzGetPoint{n3} \tkzDefPointBy[inversion = center c1 through ghost1](w2)\tkzGetPoint{w3} \tkzDefPointBy[inversion = center c1 through ghost1](t2)\tkzGetPoint{t3} %%% Reflecting the points3 across L2 \tkzDefPointBy[inversion = center c2 through ghost2](z3)\tkzGetPoint{z4} \tkzDefPointBy[inversion = center c2 through ghost2](m3)\tkzGetPoint{m4} \tkzDefPointBy[inversion = center c2 through ghost2](n3)\tkzGetPoint{n4} \tkzDefPointBy[inversion = center c2 through ghost2](w3)\tkzGetPoint{w4} \tkzDefPointBy[inversion = center c2 through ghost2](t3)\tkzGetPoint{t4} %%% Drawing T(M) \tkzDefPointBy[inversion = center o through a](m2)\tkzGetPoint{m2*} \tkzDefPointBy[inversion = center o through a](w2)\tkzGetPoint{w2*} \tkzCircumCenter(z2,m2,m2*)\tkzGetPoint{Tcz}; \tkzDrawArc[thick,color=blue](Tcz,z2)(m2); \tkzCircumCenter(m2,m2*,n2)\tkzGetPoint{Tcn}; \tkzDrawArc[thick,color=blue](Tcn,n2)(m2); \tkzCircumCenter(n2,w2,w2*)\tkzGetPoint{Tcw}; \tkzDrawArc[thick,color=blue](Tcw,n2)(w2); \tkzCircumCenter(t2,w2*,w2)\tkzGetPoint{Tct}; \tkzDrawArc[thick,color=blue](Tct,t2)(w2); %%% Drawing T(T(M)) \tkzDefPointBy[inversion = center o through a](m4)\tkzGetPoint{m4*} \tkzDefPointBy[inversion = center o through a](w4)\tkzGetPoint{w4*} \tkzCircumCenter(z4,m4,m4*)\tkzGetPoint{Tcz4}; \tkzDrawArc[thick,color=blue](Tcz4,z4)(m4); \tkzCircumCenter(m4,m4*,n4)\tkzGetPoint{Tcn4}; \tkzDrawArc[thick,color=blue](Tcn4,n4)(m4); \tkzCircumCenter(n4,w4,w4*)\tkzGetPoint{Tcw4}; \tkzDrawArc[thick,color=blue](Tcw4,n4)(w4); \tkzCircumCenter(t4,w4*,w4)\tkzGetPoint{Tct4}; \tkzDrawArc[thick,color=blue](Tct4,t4)(w4); %%% Lines of Motion \tkzCircumCenter(z,p,q)\tkzGetPoint{Cz} \tkzCircumCenter(w,p,q)\tkzGetPoint{Cw} \tkzDrawArc[very thin,dashed](Cz,q)(p) \tkzDrawArc[very thin,dashed](Cw,q)(p) \tkzDrawPoints[fill=blue](w,w2,w4) \tkzDrawPoints[size=8,fill=red](z,z2,z4) \tkzLabelPoint[below](p){\(p\)} \tkzLabelPoint[above](q){\(q\)} \tkzLabelPoint[below](z){\(z\)} \tkzLabelPoint[left = -2pt](z2){\(T(z)\)} \tkzLabelPoint[left = -2pt](z4){\(T^2(z)\)} \draw (310:2.2) node{\(L_1\)}; \draw (333:2.2) node{\(L_2\)}; \tkzDrawPoints[size=12,fill=white](p,q) \end{scope} \begin{scope}[yshift=-.8cm] \draw (0,-2) node{(a)}; \draw (6,-2) node{(b)}; \end{scope} \end{tikzpicture}