2.9: Logo cut from a circular sector

The diagram shows a company logo, $ABCD$. The logo is part of a sector, $AOB$, of a circle, centre $O$ and radius $50\text{ cm}$. The points $C$ and $D$ lie on $OB$ and $OA$ respectively. The lengths $AD$ and $BC$ are equal and $AD : AO$ is $7 : 10$. The angle $AOB$ is $\tfrac{4\pi}{9}$ radians.