\begin{tikzpicture}
              \clip (0,0) circle (2cm);
              \coordinate (o) at (0,0);
              \coordinate (A) at (2,0);
              \coordinate (p) at (90:.4);
              \coordinate (q) at (50:1.6);  
              \coordinate (r) at (300:1.4);  
              \tkzDrawCircle[dashed,color=blue](o,A)
              \hyperpbisector{p}{q}{o}{A};
              \hyperpbisector{p}{r}{o}{A};
              \hyperpbisector{q}{r}{o}{A};
              \tkzDrawPoints[size=4,fill=red](p,q,r)
              \tkzLabelPoints(q)
              \tkzLabelPoints[right](p,r)
              \draw (-1,.4) node{\(L_{qr}\)};
              \draw (-1,-1.2) node{\(L_{pr}\)};
              \draw (0,1.4) node{\(L_{pq}\)};
\end{tikzpicture}