\begin{tikzpicture}[scale=1.5]
              \clip(0,0) circle (2.2cm);
              \def\x{.5};
              \tkzDefPoint(0,0){o}
              \tkzDefPoint(2,0){a}
              \tkzDrawCircle[dashed,color=blue](o,a)
              \tkzDefPoint(180:\x){p}\tkzDefPoint(180:4/\x){p*}
              \tkzDefPoint(80:\x){q}\tkzDefPoint(80:4/\x){q*}
              \tkzDefPoint(300:\x){r}\tkzDefPoint(300:4/\x){r*}
              \tkzCircumCenter(q,r,q*)\tkzGetPoint{Cqr}
              \tkzCircumCenter(p,r,p*)\tkzGetPoint{Cpr}
              \tkzCircumCenter(q,p,q*)\tkzGetPoint{Cpq}
              \tkzInterCC(Cqr,q)(o,a)\tkzGetPoints{u1}{u}
              \tkzInterCC(Cpr,p)(o,a)\tkzGetPoints{v1}{v}
              \tkzInterCC(Cpq,q)(o,a)\tkzGetPoints{t1}{t}
              \tkzDrawArc(Cqr,u)(r)
              \tkzDrawArc(Cpq,t)(q)
              \tkzDrawArc(Cpr,v)(p)
              \tkzDefLine[perpendicular=through u,K=.-1](o,u);\tkzGetPoint{lu};
              \tkzDefLine[perpendicular=through v,K=.-1](o,v);\tkzGetPoint{lv};
              \tkzDefLine[perpendicular=through t,K=.-1](o,t);\tkzGetPoint{lt};
              \tkzInterLL(lu,u)(lv,v)\tkzGetPoint{Cuv}
              \tkzDrawArc(Cuv,u)(v)
              \tkzInterLL(lu,u)(lt,t)\tkzGetPoint{Cut}
              \tkzDrawArc(Cut,t)(u)
              \tkzInterLL(lv,v)(lt,t)\tkzGetPoint{Cvt}
              \tkzDrawArc(Cvt,v)(t)
              \tkzDrawPoints[fill=red](p,q,r)
              \tkzDrawPoints[fill=white](u,v,t)
              \tkzLabelPoint[above](u){\(u\)}
              \tkzLabelPoint[right](v){\(v\)}
              \tkzLabelPoint[left](q){\(q\)}
              \tkzLabelPoint[left](t){\(t\)}
              \tkzLabelPoint[left](p){\(p\)}
              \tkzLabelPoint[below](r){\(r\)}
              \draw (285:.25) node{\(\gamma\)};
              \draw (90:.25) node{\(\beta\)};
              \tkzLabelPoint[right](p){\(\alpha\)};
              \draw (130:.5) node{\(R_1\)};
              \draw (240:.5) node{\(R_2\)};
              \draw (350:.35) node{\(R_3\)};
              %\tkzLabelPoint[below](r)
\end{tikzpicture}