\begin{tikzpicture}
              \clip(0,0) circle (2.2cm);
              \tkzDefPoint(0,0){o}
              \tkzDefPoint(2,0){a}
              \tkzDrawCircle[dashed,color=blue](o,a)
              \tkzDefPoint(60:1.4){p}
              \tkzDefPoint(10:1.2){q}
              \tkzDefPointBy[inversion = center o through a](p)
              \tkzGetPoint{p*}
              \tkzCircumCenter(p,q,p*)\tkzGetPoint{cpq}
              \tkzTangent[at=q](cpq)\tkzGetPoint{h1}
              \tkzInterLL(q,h1)(o,p) \tkzGetPoint{c1}
              \tkzDrawCircle(c1,q)
              \tkzDefPointBy[inversion = center o through a](q)
              \tkzGetPoint{q*}
              \tkzCircumCenter(p,q,q*)\tkzGetPoint{cqp}
              \tkzTangent[at=p](cqp)\tkzGetPoint{h2}
              \tkzInterLL(p,h2)(o,q) \tkzGetPoint{c2}
              \tkzDrawCircle(c2,p)
              \tkzInterCC(c2,p)(c1,q) \tkzGetPoints{u}{v}
              \tkzClipCircle(o,a)
              \tkzDrawArc[thick,color=blue](cpq,p)(q)
              \tkzDrawCircle[color=red,orthogonal through=u and v](o,a)
              \tkzDrawPoints[size=3,fill=red](p,q,u,v)
              \tkzLabelPoint[above](p){\(p\)}
              \tkzLabelPoint[below](q){\(q\)}
              \draw (-.8,0) node{\(L\)};
              \begin{scope}[xshift=.84 cm, yshift=.68 cm, rotate=29]
              \draw (0,.14)--(.14,.14)--(.14,0);
              \end{scope}
\end{tikzpicture}