\begin{tikzpicture}
\clip(0,0) circle (2.3cm);
\tkzDefPoint(0,0){o}
\tkzDefPoint(2,0){a}
\tkzDefPoint(70:2){u}
\tkzDefPoint(250:2){u1}
\tkzDefPoint(340:2){v}
\tkzDefPoint(160:2){v1}
\draw(u1)--(u);
\draw(v1)--(v);
\tkzDrawCircle[dashed, color=blue](o,a)
\tkzDrawPoint[fill=red](o)
\tkzDrawPoints[fill=white](u,v)
\tkzLabelPoint[above](u){\(u\)}
\tkzLabelPoint[right](v){\(v\)}
\tkzLabelPoint[below left](o){\(0\)}
\tkzDefLine[perpendicular=through u,K=1](o,u)\tkzGetPoint{x1}
\tkzDefLine[perpendicular=through v,K=1](o,v)\tkzGetPoint{x2}
\tkzInterLL(u,x1)(v,x2)\tkzGetPoint{c}
\tkzClipCircle(o,a)
\tkzDrawCircle(c,u)
\tkzDrawPoints[fill=white](u,v)
\draw (30:1) node{\(L\)};
\end{tikzpicture}