3.7: Circle with midpoints and an inner arc

The diagram shows a circle, centre $O$, radius $2a$. The points $A$ and $B$ lie on the circumference of the circle. The points $C$ and $D$ are the mid-points of the lines $OB$ and $OA$ respectively. The arc $DC$ is part of a circle centre $O$. The chord $AB$ is of length $2a$.