\begin{tikzpicture}
              \tkzDefPoint(0,0){o}
              \tkzDefPoint(2,0){A}
              \tkzDefPoint(-2,0){B}
              \tkzDefPoint(40:2){u}
              \tkzDefPoint(220:2){ua}
              \tkzDrawCircle[solid,color=brown](0,A)
              \draw[thick,->](89:2)--(90:2);
              \draw[thick,->](269:2)--(270:2);
              \draw (A)--(B) (u)--(ua);
              \tkzDrawPoints[size=6](A,B)
              \fill[fill=blue,opacity=0.1] (A) to (o) to (u) to [bend left=20] (A);
              \fill[fill=blue,opacity=0.1] (B) to (o) to (ua) to [bend left=20] (B);
              \tkzDrawPoints[size=8,fill=red](o)
              \draw (20:.5) node{$\alpha$};
\end{tikzpicture}