\begin{tikzpicture}
                  \clip(0,0) circle (2.2cm);
                  \tkzDefPoint(0,0){o}
                  \tkzDefPoint(2,0){A}
                  \tkzDefPoint(-2,0){B}
                  \tkzDefPoint(110:2){u}
                  \tkzDefPoint(290:2){ua}
                  \tkzDefPoint(160:2){v}
                  \tkzDefPoint(340:2){va}
                  \coordinate (m1) at ($(u)!.5!(ua)$);
                  \coordinate (m2) at ($(v)!.5!(va)$);
                  \coordinate (cu) at ($(m1)!-1!90:(ua)$);
                  \coordinate (cv) at ($(m2)!-1!90:(va)$);
                  \tkzInterCC(cu,u)(cv,v)\tkzGetPoints{p}{q}
                  \tkzDrawCircle[solid,color=brown](0,A)
                  \draw[thick,->](89:2)--(90:2);
                  \draw[thick,->](269:2)--(270:2);
                  \tkzDrawPoints[size=6](A,B)
                  \tkzClipCircle(0,A)
                  \tkzDrawCircle(cu,u)
                  \tkzDrawCircle(cv,v)
                  \fill[fill=blue,opacity=0.1] (u) to [bend right=20.3]  (v) to [bend left=23] 
                  (p) to [bend right=15] (u);
                  \fill[fill=blue,opacity=0.1] (ua) to [bend right=23]  (p) to [bend left=18] 
                  (va) to [bend left=21] (ua);
                  \tkzDrawPoints[size=8,fill=red](p)
                  \draw (.3,.9) node{$\alpha$};
\end{tikzpicture}